Mathematical Literacy DATA HANDLING

MATHEMATICAL LITERACY Grade 12 SELF STUDY GUIDE BOOKLET 1B Data handling 1

TABLE OF CONTENTS Table of Contents Page 1. Introduction 3 2. How to use this self-study guide 4 3. Data Handling 3.1.1 Key concepts 6 - 10 3.1.2 Summarising data 11 - 19 3.1.3 Measures of spread 20 - 26 3.1.4 Representing data 27- 32 3.2 Solutions to practice questions 3.2.1 Summarising data 33 - 37 3.2.2 Measures of spread 38 - 40 3.2.3 Representing data 41 - 44 4. Examination guidance 45 - 46 5 Study and Examination Tips 48 6 References 49 7 Acknowledgements 50 2

1. Introduction The declaration of COVID-19 as a global pandemic by the World Health Organisation led to the disruption of effective teaching and learning in many schools in South Africa. The majority of learners in various grades spent less time in class due to the phased- in approach and rotational/ alternate attendance system that was implemented by various provinces. Consequently, the majority of schools were not able to complete all the relevant content designed for specific grades in accordance with the Curriculum and Assessment Policy Statements in most subjects. As part of mitigating against the impact of COVID-19 on the current Grade 12, the Department of Basic Education (DBE) worked in collaboration with subject specialists from various Provincial Education Departments (PEDs) developed this Self-Study Guide. The Study Guide covers those topics, skills and concepts that are located in Grade 12, that are critical to lay the foundation for Grade 12. The main aim is to close the pre-existing content gaps in order to strengthen the mastery of subject knowledge in Grade 12. More importantly, the Study Guide will engender the attitudes in the learners to learning independently while mastering the core cross-cutting concepts. 3

2. How to use this Self Study Guide. • This study guide covers selected sections of data handling which form part of paper 1. • The topic is drawn from the CAPS Grade 10 – 12 curricula. Selected sections are presented in the following way: o What you should know at the end of the section. o Explanation of key concepts. o Summary/Notes. o Worked examples. o Practice questions. o Solutions to practice questions. • Mathematical Literacy is a highly contextualised subject. Whilst every effort has been taken to ensure that the skills and concepts you will be examined on, are covered in this study guide, it is in fact the context used in the examination that will determine how these skills and concepts are assessed. • This study guide covers all the cognitive levels. • Go through the worked examples on your own. • Do the practice examples on your own. Then check your answers. • Read symbols and explanation table below to understand how marks are allocated. Symbol Explanation M Method M/A Method with accuracy MCA Method with consistent accuracy CA Consistent accuracy A Accuracy C Conversion S Simplification RT/RG/RD Reading from a table/graph/diagram SF Correct substitution in a formula O Opinion/Example/Definition/Explanation P Penalty, e.g. for no units, incorrect rounding off, etc. R Rounding off NPR No penalty for rounding NPU No penalty for the units AO Answer only, if correct, full marks 4

• Reward yourself for the things that you get right. • If any of your answers are incorrect, make sure that you understand where you went wrong, before moving on to the next section. • The study guide covers both generic and subject specific examination tips. You are expected to read and understand the tips, so that you are able to study more effectively. 5

3.1 Data handling 3.1.1 Key Concepts DATA HANDLING TERMS MEANING Bar graph The graphical representation of data that uses bars to compare different categories of data. 90° graph using bars to show frequencies (horizontal and vertical graph), the vertical heights of a set of bars of equal breath represent the values of the dependant variable in a data set. Biased question Biased question is the question containing factors that may influence the respondent to answer in a way that is not entirely true. Box-and-whisker Diagram that statisticians use to show the distribution of data along a number line plot divided into quartiles. Broken line graph A graph that has numbers that alternate going up and down and do not keep to a curved consistent line. Categorical data The data that is given in the form of words, names, or labels. It is generally descriptive in nature, as data classified and organized into categories. Class Interval Data that is divided into a smaller number of categories Classify Identify the type or class. Compound bar (Also referred as vertical stack graph or component bar chart) display two or more graph sets of data. However, it shows a part/whole relationship so you can easily see what amount each data group makes up of the whole. Continuous data The data that that is given as numbers including the decimal numbers and/or fractions. Numerical data (measurements like weight or age). Data Information, series of observations, measurements, facts; collection and recording of information for statistical investigation. It is raw information that has been collected, without any organization or analysis. Data collection Two-column table showing what is observed and how many times it was observed; sheet items of information. Data handling Data handling refers to the process of collecting, organizing, summarizing, representing, and analyzing information. Discrete Separate; distinct; opposite of continuous. Discrete data Numerical data (fixed numbers like size of family). Data that can have only certain values (quantities that can be counted, usually whole numbers). Double bar graph The most common multiple bar graph that compares two sets of data. Frequency (f) Number of times a data value is recorded. Frequency table Table showing frequencies in organised form. Table summarising the frequencies of all the data values in a data set. Group Put into classes, sort, arrange, organise. Grouped data The data given in the form of intervals. Histogram 90° graph using adjacent bars to show frequencies of continuous numerical data with many different values. Areas of rectangles (continues; no gaps between them) show frequency of classes of data. The graphical representation of continuous numerical data by way of bars to display the frequency of the items in the data set. 6

Horizontal bar 90° bar graph using horizontal bars to compare or rank items like household sizes in graph a block of flats. Impossible No chance of the outcome happening e.g. getting a 7 with an ordinary six-sided outcome dice. Interview Record data by talking to someone face to face or over the telephone. Inter-quartile The difference between quartile 3 and quartile 1 range OR The difference between largest quartile and the smallest quartile. Investigate Examine; look into; study. Line graph A graph that uses line segments to connect data points and shows changes in data over time. Maximum value The highest or biggest value in the data set. Mean Average of the values in a data set; sum of all the observed values divided by the number of observations. Mean [of a set of Average: sum of all data values divided by the number of data values. data] Measures of Numbers that tell more about the balance (middle values) in a data set (mode; central tendency median; mean). Measures of Numbers that tell how far data values in a data set lie apart; spread of numerical spread data set (range, quartiles, and percentiles). Median Middle value in an ordered data set. Median [of a set Value that cuts an ordered data set in half. of data] Methods of Methods of collecting data is interview, observation and research or survey. collecting data Minimum value The lowest or smallest value in the data set. Mode Value or values appearing most often in a data set. Mode of a set of Most common data value in a data set. data Multiple bar A bar graph that displays two or more sets of data at once for easy comparison graph Numerical data The data that is given in the form of numbers. Observation Recording of data by watching someone or something closely. OR The method of collecting data that involves watching, listening, touching, reading. Outcome Result of a trial (experiment). Outcome [fair] All outcomes are equally likely to occur. Outliers Data value that lies an abnormal distance from the other data values in the data set. OR Extreme low or extremely high value in the data set. OR The item or value in the data set that differs significantly with other items or values. Percentiles The points that divide the data set into 100 equal parts. Quartile 1 is the 25Th percentile i.e., the value at which 75% of the data set lies above and 25% of the data set lies below it. Quartile 2 Is the 50th percentile i.e., the value at which 50% of the data set lies above and 50% of the data set lies below it. Quartile 3 is the 75th percentile i.e., the value at which 25% of the data set lies above and 75% of the data set lies below it. 7

Qualitative data/ Data that relates to certain categories e.g. male/female or type of car etc. Categorical data Quantitative data/ Data that can be measured and can be discrete or continuous. Numerical data Quartiles The values that divide a list of numbers into four equal parts. Questionnaire List of questions that can be used to collect data. An instrument consisting of questions for the purpose of collecting data. Random The sampling method that allows every member of the population a chance of being sampling included in the sample. Range [of a data Difference between the highest and lowest values in a data set. set] OR The difference between the maximum value and the minimum value in the data set. Related [data Linked; connected. sets] Represent[data] Draw; graph. Representative Sample likely to give results similar to those obtained from studying the whole sample population. Sample Subset (small group) chosen from the population to represent the population. OR The fraction of the entire group to be used in the collection of data Sampling Choosing a representative sample. Scatter plot A graph that is made by plotting ordered pairs in a coordinate plane to show the relationship between two sets of data, but the points are not connected by a line. Sort Put, organise into categories. Stacked bar (Also known as stacked bar charts) Instead of displaying a compound bar graph with graph bars side-by-side, a stacked bar graph divides the bar into segments. It is used to show how one bar is divided into smaller parts. Survey Collect data from a group of people or objects. Survey [biased] Survey containing factors that produce answers that do not represent a truthful picture of the situation. Ungrouped data The data given as individual items or values. 8

3.1.2 SUMMARISING DATA OBJECTIVES At the end of this section, you must be able to do the following: • Calculate the mean. • Calculate the median. • Identify the mode for arranged data. • Calculate the range. • Analyse measures of central tendency and make deduction about the trends in the data Summary Summarising Data Once the collected data has been classified and organised, it is important to summarise the data, in order to provide additional information regarding the trends of the data set. Measures of Central Tendency There are 3 measures of central tendency § Mean § Median § Mode MEAN § the formula used: sum of all values in data set Mean = total number of values in data set § It can be only be calculated if the data set is numerical MEDIAN § All data values must be arranged in ascending order. 9

§ The median is the middle value of an ordered data set. § It can be calculated if the data set is numerical MODE § The mode is the data value(s) that occur(s) most frequently in a set. § If two values occur most frequently, then the data set is referred to as bimodal. § It can be determined for both numerical and categorical data. RANGE § The range of data indicates the difference between the highest and the lowest values in the data set. Range = highest value – lowest value § If the range is small, the data is clustered together; and if the range is larger, then the data is more spread apart. NOTE: Range is not part of Measures of Central Tendency but Measures of Spread Worked examples 1 1. Mr Khabo’s Grade 12G Mathematical Literacy class test marks out of 20 are as follows: 18; 12; 15; 15; 15; 17; 18; 19; 20 1.1 Calculate the mean. 1.2 Find the median of the data set. 1.3 Write down the mode. 1.4 Determine the range. 10

Solutions 1.1 12 + 15 + 15 + 15 + 17 + 18 + 18 + 19 + 20 Mean = 9 149 = 9 =16,6 1.2 17 1.3 15 1.4 Range = Highest – Lowest = 20 – 12 =8 Worked examples 2 2. Mr Khabo’s Grade 12G Mathematical Literacy examination marks out of 100 are as follows: 50; 26; 72; 37; 53 ;23 ;89 ;67; 53; 42 2.1 Calculate the mean. 2.2 Arrange the marks in ascending order. 2.3 Write down the mode. 2.4 Determine the range. 2.5 Find the median of the data set. 11

Solution 2.1 50 + 26 + 72 + 37 + 53 + 23 + 89 + 67 + 53 + 42 Mean = 10 512 = 10 =51,2 2.2 23; 26; 37; 42; 50; 53; 53; 67; 72; 89 2.3 53 2.4 Range = Highest – Lowest = 89 – 23 = 66 2.5 50 + 53 Median = 2 103 = 2 =51,5 12

Practice Questions Question 1 1. The data below represents the points accumulated during the 2017 University female hockey and soccer tournament. TABLE 1: Accumulated points by hockey and soccer in the tournament Teams Up Tuks Maties NWU Puk Wits UFS Kovsie UJ Madibas UKZN Hockey 18 18 18 12 9 6 3 0 Soccer 11 17 11 6 12 9 12 0 [Source: Varsity Sports] Use the Table 1 from above to answer the questions that follow. 1.1 Arrange the soccer points in descending order. (2) 1.2 Identify the teams that accumulated less points in hockey than in soccer during the tournament. (2) 1.3 Determine the mode of the soccer points. (2) 1.4 Calculate the mean of the hockey points. (3) 1.5 If the tournament points for the two sporting codes are chosen at random, determine the probability (as a common fraction) that the points will be less than 10. (2) [11] 13

Question 2 Moipone, a Grade 10 learner conducted a research about Top achievers of Mpatleng Secondary School after attending the award ceremony held on the 11 October 2019 when Seboko M received an award again. She found that from 2013 the school held the award ceremony for the best learners. The 2013 and 2017 best learners were among the top 100 in the Free State Province. Year 2013 2014 2015 2016 2017 2018 Name Mompe Domkrag T Nyila P Maleho k Thapong S Seboko M Average % 85 72 69 71 78 72 Grade 12 12 12 12 12 11 Use the table from above to answer the questions that follow. 2.1 Find the median of average percentage of best learner. (3) 2.2 Show that the best learner average percentage mean it’s 75%. (4) 2.3 Give the modal average percentage, and compare with the median. (2) 2.4 Determine the range. (2) 2.5 Use the table of best learner above to determine the probability (as decimal) of randomly selecting a learner appeared in Top 100 of the province. (3) 14

Question 3 Mrs Bush wanted to encourage Mr Bush to drive carefully while on holiday. She showed him some statistics which represents the number of accidents occurring across South Africa. The statistics are reflected in TABLE 4. TABLE 4: Statistics of road accidents from 1 December to 11 January 2015/2016 Year PROVINCES GP KZ-N WC EC FS MP NW LP NC TOTAL SA 2015/2016 246 308 122 227 131 159 108 186 A 1535 2016/2017 271 B 162 278 157 184 136 208 57 C Difference 25 -6 40 51 26 25 28 22 9 220 Use TABLE 4 from above to answer the questions that follow. 3.1 Calculate the value of A. (2) 3.2 Determine the value of B. (2) 3.3 Hence determine the value of C. (2) 3.4 Determine the mean number of accidents in 2015/2016. (3) 3.5 Determine the median for the difference in road accidents reported. (2) 3.6 What is the probability that the number of accidents for 2016/2017 will drop the following year? (2) 15

Question 4 Neo opened a car wash business and decided to observe the different types of cars that come for a wash on a particular Saturday and Sunday. Table 2 below shows his findings: TABLE 2: TYPES OF CARS WASHED AT A CAR WASH ON SATURDAY AND SUNDAY Number of cars washed Number of cars washed Type of car on Saturday on Sunday Jaguar 2 4 Mercedes Benz 5 6 BMW 6 6 Renault 4 3 Toyota 18 15 TOTAL 35 34 Use the information above to answer the following questions: 4.1 Write down the data collection method used to collect the data above. (2) 4.2 State whether the number of cars washed represent discrete or continuous data. (2) 4.3 Calculate the number of cars that were washed altogether on Saturday and (2) Sunday? 4.4 Write down the probability of a worker washing a Renault car on a Saturday. (2) [08] 16

Question 5 Sipho and Sandile recorded their times in minutes for a number of 7 km trial runs. TABLE 6: Times taken for a 7 km trial run Sandile (in 35 32 31 32 32 31 30 29 32 30 minutes) Sipho (in 30 31 32 33 33 34 34 35 35 35 37 minutes) Use TABLE 6 from above to answer the questions that follow. 5.1 Write down Sipho's median time. (2) 5.2 Calculate Sandile's median time. (3) 5.3 Determine the range of Sipho's time. (2) 5.4 Calculate Sandile's mean time, rounded off to TWO decimal places. (3) 5.5 Determine the mode of the times taken by Sandile. (2) 5.6 Use Sipho's times for his eleven trial runs to determine the probability that his next (2) trial run will be less than 35 minutes. [14] 17

3.1.3 MEASURES OF SPREAD OBJECTIVES At the end of this section, you must be able to do the following: • Identify the minimum and the maximum value. • Calculate the quartiles (Q1, Q2 and Q3). • Analyse measures of spread and make deduction/s about the trends in the data. SUMMARY Measures of Spread There are two measures of spread: • Range • Interquartile Range INTERQUARTILE RANGE (IQR) • The IQR is the difference between the upper quartile (Q3) and the lower quartile (Q1). IQR = Q3 – Q1 • Lower quartile (Q1) is 25% mark. • Median (Q2) is 50% mark • Upper quartile (Q3) is 75% mark • If the IQR is a low number, the middle 50% of the data is close together/clustered. • If the IQR is a high number, the middle 50% of the data is far apart/spread out. Before you can calculate the interquartile range, you first need to determine the quartiles of the data. 18

QUARTILES • All data values must first be arranged in ascending order (from smallest to highest). • Quartiles divide a data set into four equal parts. Ø Middle quartile (Q2) is the median of the data set. Ø Lower quartile (Q1) indicates the first quarter of the data set. Ø Upper quartile (Q3) indicates the upper quarter of the data set. Worked example 1 The final Grade 12 results for Ntema and Khati are given below: Ntema 85% 68% 57% 79% 92% 72% 60% 43% 50% Khati 78% 29% 45% 55% 83% 72% Use the above table to answer the following questions: 1.1 Calculate the quartiles for each set of data 1.2 Determine the interquartile range for each data set. 19

Solutions 1.1 Ntema 43; 50; 57; 60; 68; 72; 79; 85; 92. Q2 = 68% 50 + 57 Q1 = 2 107 = 2 = 53.5 79 + 85 Q3 = 2 164 = 2 = 82 Khati 29;45; 55; 72; 78 ;83 55 + 72 Q2 = 2 127 = 2 = 63,5 Q1 = 45 Q3 = 78 2.2 Ntema IQR = Q3 – Q1 = 82 – 53,5 = 28,5 Khati IQR = Q3 – Q1 = 78 – 45 = 33 20

Practice Questions Question 1 Mr Mokebe, a Grade 12 educator, teaches learners about the Body Mass Index (BMI). He brings a digital bathroom scale and a measuring tape to class. Table 1 shows the weight of 60 learners in three classes. TABLE 1: Weight of learners in 12A, 12B and 12C classes. 50 48 55 53 55 56 51 60 62 57 12 A 52,5 60 58 43 47 50 51 58 55,5 60 40 42 46 46 48 48 51 51 51 52 12 B 53 55 57 58 60 60,2 61 64 68 70 43 47 48,1 49 50 52 53,1 53,6 54 56 12 C 56,2 57 60 60 61 61 63 63 65 65 Use TABLE 1 from above to answer the following questions. 1.1 The mean (average) weight of learners in 12A. (3) 1.2 The modal weight of learners in 12B. (2) 1.3 The median weight of learners in 12C. (3) 1.4 Calculate the quartile 1 and the quartile 3 for 12C. (4) 1.5 Hence calculate the interquartile range for 12 C. (2) 1.6 Show by calculations that the range for the weight of 12A class is 19 kg. (2) 21

Question 2 The data in the tables below represent the distance (in km) that the learners from Exhibition High School walked to school the morning before a Mathematical Literacy test, and the marks (out of 50) that they obtained for the test. TABLE 1 : Distance (in km) travelled by learners 0,2 0,5 0,3 1,2 0,25 0,75 1,3 3 1,2 1,8 2,4 1,5 0,2 0,8 2,6 3 1,4 0,75 0,5 1,2 3,2 0,8 0,3 1 1,8 TABLE 2 : Marks obtained for the test 49 38 37 30 39 34 29 19 27 25 20 28 43 33 41 15 25 38 40 30 18 30 39 28 28 Use TABLE 1 and TABLE 2 from above to answer the questions that follow. 2.1 Identify the SECOND shortest distance walked by a learner. (2) 2.2 Determine the highest mark scored by a learner. (2) 2.3 Name ONE data collection instrument used to collect this data. (2) 2.4 Determine the median of the test marks. (3) 2.5 Determine the mode of the test marks. (2) 2.6 Calculate the mean mark for this test. (3) 2.7 Determine the probability of randomly selecting a learner who walked less than 1 km on the day of the test. (2) 2.8 Determine the probability of randomly selecting a learner who scored more than 35 out of 50 for the test. Write your answer as a decimal. (2) 22

Question 3 TABLE 5 below shows the results of a recent gymnastics competition held at a school. The table shows the gymnasts' names, teams, divisions and various events with total scores given to three decimal places. TABLE 5: RESULTS OF A GYMNASTICS COMPETITION EVENTS TOTAL SCORE GYMNAST TEAM DIV. VAULT BARS BEAM FLOOR Senior G Gilliland GTC 9,550 9,100 9,400 9,625 37,675 A Junior H Radebe Olympus 9,450 9,250 8,900 9,400 37,000 B Junior L Gumede Olympus 9,475 9,300 8,700 9,500 36,975 A Senior S Rigby TGA 9,500 8,650 8,925 9,350 36,425 A Senior H Khumalo GTC 9,300 9,100 A 9,225 36,425 A Junior C Maile Olympus 8,950 9,050 9,025 9,375 36,400 A Senior M Stolp GTC 9,400 8,750 8,725 9,500 36,375 A Junior M McBride GTC 9,475 9,050 8,700 9,050 36,275 A Senior A Boom TGA 9,650 8,300 8,700 9,500 36,150 A Junior B Makhatini Olympus 9,350 9,200 9,150 9,350 37,050 B 23

Use TABLE 5 from above to answer the questions that follow. 3.1 Identify the team that achieved the highest score for the vault event. (2) 3.2 Determine the range of G Gilliland's scores. (2) 3.3 Calculate the mean score for the bar event. (3) 3.4 Determine missing value A. (3) 3.5 Write down the modal score for the total points scored. (2) 3.6 Determine, as a percentage, the probability of selecting a gymnast in the Junior division with a total score of more than 36,970. (3) 3.7 Calculate the value of quartile 2 for the floor event. (3) 24

3.1.4 REPRESENTING DATA OBJECTIVES At the end of this section, learners must be able to do the following: • Identify the minimum and the maximum value. • Calculate IQR. • Interpret the box-and-whisker plot. SUMMARY Representing data BOX – AND – WHISKER PLOTS • The box-and-whisker plot is a visual representation of the 5-number summary of a data set. • The 5-number summary is made up of the following data values: 1. Minimum value 2. Q1 (lower quartile) 3. Q2 (median) 4. Q3 (upper quartile) 5. Maximum value Visual representation Q1 Q2 Q3 Min value Max value NOTE: You are only expected to interpret the box-and-whisker plot, you will not be expected to draw the box-and-whisker 25

Worked example 1 1 The following box – and - whisker plot represents the summary of data collected about the amount of rand saved by the learners in a certain school in the ordinary public school sector. One hundred and forty (140) people took part in this survey Study the box-and-whisker plot above and answer the questions that follow: 1.1 Why is it important for a learner to save money? 1.2 What percentage of the people saves more than R65 per month? 1.3 Calculate the value of inter-quartile range 1.4 Busi claims that 70 people save between R15 and R35. Verify, showing ALL calculations, whether her statement is valid. Solution 1.1 It will assist learners to buy bigger articles like bicycles, cell phones etc. for which their pocket money is not enough any other reasonable answer 1.2 25% 1.3 IQR = 65-25üM = 40üCA 1.4 50 ´140 40 = 70 people Her statement is correct 26

Practice Questions Question 1 The box-and-whisker diagrams representing the percentage achieved in the exam of the two Mathematical Literacy Grade 12 classes consisting of 26 learners each are shown below: Class A Class B 0 10 20 30 40 50 60 70 80 90 100 The arranged percentage marks of class A are given below: 19,8 26 27,9 28 29,8 30 30,1 49 49,7 49,7 49,8 52 53,3 X 66,7 66,8 66,9 H 75 79,9 79,9 80 80 80 84 89,9 1.1 Calculate the missing values of: X, by reading the median value from the box-and-whisker plot H, if the mean percentage mark of Class A is 57,1 (6) 1.2 Calculate the probability of randomly selecting a learner from Class A with (2) a mark less than 79,9%. 1.3 Compare the Inter Quartile Ranges (IQR) of Class A and Class B. (5) [13] 27

Question 2 After the first term a Mathematical Literacy test was written at Matlwangtlwang Secondary School in Steynsrus. The Head of department sampled the scripts of 24 learners out of 84 learners. The results of these 24 learners were as follows. The test was out of 60 marks. The arranged test results and a corresponding box and whisker diagram are given below. 8 14 15 15 16 16 17 18 19 20 20 20 22 23 24 24 25 26 30 35 35 35 35 36 Minimum value Maximum value A B C Use only the results of the sample to answer the following questions: 2.1 Calculate the range of the learners' marks. (2) 2.2 Determine the median mark of the learners. (2) 2.3 What is the modal mark of the learners? (2) 2.4 Calculate the mean mark of the learners. (3) 2.5 Write down the minimum value and maximum value of the box and whisker diagram (2) 2.6 Calculate the missing quartile values A, B and C of the box and whisker diagram. (5) 2.7 Calculate the interquartile range of the learners' test. (2) 28

Question 3 The majority of Metro High Schools’ learners who committed violent incidents wereGrade 9 boys. The arranged ages of these Grade 9 boys and a corresponding box-and- whisker plot aregiven below. A 14 14 14 14 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 17 17 17 17 17 17 17 17 17 17 17 17 17 18 18 18 18 18 18 18 B C D [Adapted from the South African School Administration and Management System] Use the information given above to answer questions that follow. 3.1 Determine the missing value A if the range of the ages of the Grade 9 boys who committed violent incidents is 5 years. (2) 3.2 Calculate the mean age of the Grade 9 boys who committed violent incidents. (3) 3.3 Calculate the missing quartile values B, C and D of the box-and-whisker plot. (5) 3.4 A Grade 9 boy who committed a violent act is randomly selected. Determine the probability (expressed in decimal form) that the boy would be 16 years or older. (3) 3.5 Give a possible reason why so many Grade 9 boys at Metro High School (2) committed violent incidents. 29

Question 4 The box-and-whisker diagram that represent the marks achieved in a Mathematical Literacy Test for a Grade 12 class consisting of 20 learners is shown below: 4 19,5 22 28 50 D 5 3 d D D information given above to answer questions that follow. Use the d 4.1 Write d down the lowest score obtained. (2) d 4.2 Define the term range in the context of the information provided. (2) c 4.3 cWhat percentage of learners scored between 4 marks and 19,5 marks? (2) C 4.4 Determine the number of learners who scored marks that are less than D the 3rd quartile. (3) C 4.5 IfCa mark of a learner falls on the 2nd Quartile (Q2), what does this mean? (2) C C 30

3.2 SOLUTIONS TO PRACTICE QUESTIONS 3.2.1 SUMMARISING DATA Question 1 Q Solution/s Explanation L 1.1 17 12 12 11 11 9 6 0 üüA 1 A all values in correct order L2 1 A Descending (2) 1.2 UFS Kovsie 2 A all correct L2 UJ üüA -1 for every one omitted Madibas -1 for every incorrect answer -1 for every extra team mentioned. (2) 1.3 12üA and 11üA A 12 L2 A 11 (2) 1.4 !" 1 A 84 L2 Mean = üM üA ! 1 M divide total by 8 = 10,5 üCA 1 CA answer (3) 1.5 7 1A Numerator L2 üüA 1A Denominator 16 (2) 31

Question 2 Q Solution/s Explanation L 2.1 69; 71; 72; 72; 78; 85 P 1 Arrangement L3 72 + 72 PM 1M Median = 1Answer 2 = 72PA (3) 2.2 69 + 71 + 72 + 72 + 78 + 85 1MA L4 Mean = P 1A 447 6 1M dividing by 6 447 = PP 1Answer 6 (4) = 74.5PA 2.3 72PA 1Answer 72 L2 They are the same RP 1Reason (2) 2.4 1Method L1 Range = 85 – 69PM 1Answer (2) = 16PA 2.5 1 Numerator L2 2 PA 1Denominator Probability = 1CA Answer 6 PA (3) =0.33 PCA 32

Question 3 Q Solution/s Explanation L 3.1 1 535 – 1 487 ü M 1Method L2 A = 48 üA 1A Answer OR A = 57-9üM = 48üA (2) 3.2 B = 308 + (-6) üM 1M Addition L2 = 302üA 1A Answer (2) 3.3 C = 271 + 302 + 162 + 278 + 157 + 184 + 136 + 20 üM 1M Addition L2 = 1 755 üA 1A Answer OR 1 535 + 220üM = 1 755üA (2) 3.4 1SF Correct values L2 246 + 308 + 122 + 227 + 131 + 159 + 108 + 186 + 48 Mean = üSF 1M Dividing by 9 9 1535 = 1A Answer 9 PM = 170,56üA (3) 3.5 1M Arrange in ascending/ L2 -6; 9; 22; 25; 25; 26; 28; 40; 51 üM descending order Median = 25 üA 1A Answer (2) 3.6 Unlikely üA 1A Answer L2 Most of the accidents increased from 2015/16 to 2016/17. ü J 1J Reason (2) 33

Question 4 Q Solution/s Explanation L 4.1 L1 Observation üüA 2A correct method (2) 4.2 L1 DiscreteüüA 2A discrete (2) 4.3 No. of cars washed = 35 + 34üMA 1MA adding correct values L1 = 69üCA 1CA total number of cars OR 1MA adding all values No. of cars washed = 2 + 5 + 6+ 4 +18 +4+6+6+3+15 üMA 1CA number of cars = 69 üCA (2) 4.4 1A numerator L1 4 üA 1Adenominator Probability = 35 üA (2) 34

Question 5 Q Solution/s Explanation L 5.1 2A Correct median L1 Median time = 34 minutes PPA (2) 5.2 1A arranging in order L3 Sandile:29; 30; 30; 31; 31; 32; 32; 32; 32; 35 PA 1M calculation Median time = 31 + 32 PM 2 1CA solution = 31,5 PCA (3) 5.3 1M method L2 Range = 37 – 30 PM 1A correct Range (2) =7 minutes PA 5.4 1M concept of L2 Sandile’s PM mean 29 + 30 + 30 + 31 + 31 + 32 + 32 + 32 + 32 + 35 Mean = 1A addition 10 314 PA = 1 CA solution 10 (3) = 31,4 PCA 5.5 Mode = 32 minutes 2A correct mode L1 5.6 L2 7 PA 1A Numerator Probability = 1 A Denominator 11 PA (2) 35

3.2.2 MEASURES OF SPREAD Question 1 Q Solution/s Explanation L 1.1 50 + 48 + 55 + ......60 PM 1M adding all values L2 Mean for 12 A = 20 1M dividing by 20 1082 = PM 20 1A Answer = 54,1 PA (3) 1.2 Modal weight for 12B = 51 2A answer L2 (2) 1.3 L2 56 + 56,2PM 1M identifying 56 Median for 12C = and 56,2 2 PM 1M dividing by 2 = 56,1PA 1A answer (3) 1.4 50 + 52 2A answer L1 Q1 = 2 = 51 PPA 61 + 61 Q3 = 2A answer 2 = 61 PPA (4) 1.5 1M IQR concept L1 Interquartile range (12C) = 61 – 51 PM 1CA answer = 10 PCA (2) 1.6 Range for 12A = 62 – 43 PPM 2M Range Concept L1 = 19kg (2) 36

Question 2 Q Solution/s Explanation L 2.1 0,25 km OR 250 m üüRT 2 RT L1 (2) 2.2 49 üüRT 2 RT L1 (2) 2.3 Questionnaire üüA 2A L1 OR Survey (2) 2.4 15; 18; 19; 20; 25; 25; 27; 28; 28; 28; 29; 30; 30; 1M arranging all correct values L2 30; 33; 34; 37; 38; 38; 39; 39; 40; 41; 43; 49 üM Median = 30 üüA 2A correct median (3) 2.5 Mode(s) = 28 and 30 üüA 2A L1 (2) 2.6 Mean 1 A addition of all correct L2 üA values 783 1 MA dividing by 25 = 25 üMA 1CA final answer = 31,32 üCA (3) 2.7 2A Answer L2 11 OR 44% OR 0,44 üüA 25 (2) 2.8 9 2A Correct decimal L2 = 0.36üüA 25 (2) 37

Question 3 Q Solution Explanation L 3.1 TGA – teamüüRT 2RT correct team L1 (2) 3.2 üRT L1 Range = 9,625 – 9,100 1RT reading = 0,525 üCA correct values 1CA concept of range (2) 1RT adding correct L2 Mean = üRT üM values 9,100 + 9,250 + 9,300 + 8,650 + 9,100 + 9,050. + 8,750 + 9,050 + 9,200 + 8,300 1M concept of 10 mean = 8,975 üCA 1CA simplification (3) 3.4 A = 36,425 – (9,300 + 9,100 + 9,225) üRT 1RT correct values L1 = 8,800 üA 1M adding and subtracting 1A simplification (3) 3.5 36,425 üüA 2A correct mode L1 (2) 3.6 1A numerator L2 3üA 1A denominator ´100 1A percentage 5üA = 60%üA (3) 3.7 üRT 1RT correct values L2 üRT 9,375 + 9,400 1M dividing by 2 Quartile2 = 2 üM 1A simplification = 9,3875 üA (3) 38

3.2.3 REPRESENTING DATA Question 1 Q Solution/s Explanation L 1.1 PMA 1MA median concept. L3 53,3 + X 1RG median Median = = 60 PRG 1CA value 2 => X = 66,7 PCA sum of the marks Mean = 1MA mean concept total number of learners 1CA adding values PCA 1CA value of H 1410,9 + H 57,1 = 26 PMA 1484,6 =1410,9 + H (6) H = 73,7PCA 1.2 L2 19 PCA 1CA numerator P(more than 79,9%) = 1MA denominator 26 PMA = 0,731 OR 73,1% (2) 1.3 L1 Class A: Q1 = 30 PA 2A identification of quartiles Q3 = 80 PA IQR A Class = 80 – 30 1CA IQR = 50 PCA Class B: Q1 = 20 Q3 = 70 IQR Class B = 70 – 20 1A IQR value = 50 PA 1J compare Both classes have the same IQR.PJ (5) 39

Question 2 Q Solution/s Explanation L 2.1 Range = Highest - Lowest 1SF L2 = 36 – 8 PSF = 28 PCA 1CA (2) 2.2 1M median concept L2 20 + 22 PM Median = 2 =21 PA 1 CA (2) 2.3 Modal mark = 35yrs PPA 2A L2 (2) 2.4 1A adding all values L2 548 PA Mean mark = 1 A dividing by 24 24 PA = 22,83 PCA 1 CA simplification (3) 2.5 1A identify Min value L1 Minimum = 8 PRT 1A identify Max value Maximum = 36 PRT (2) 2.6 L2 16 + 17 PRT 1A identify correct values A= 2 = 16,5 PCA 1CA answer B = 21 PA 1A answer 1A identify correct values 26 + 30 PRT C= 1 CA answer 2 (5) = 28 PCA 2.7 1 MA subtract L2 IQR = 28 – 16,5 P MA 1A =11,5 PA (2) AA AM M Question 3 M M M M; 40

Q Solution/s Explanation L 3.1 Range = Highest - Lowest 1M concept of range L2 5 = 18 – A PM A = 13 1CA value of A PCA OR OR PM A = 18 – 5 = 13 PCA 1M concept of range using 5 1CA value of A (2) 3.2 CA answer from 3.1 L2 1M adding all 40 values 13 + 14 ´ 4 + 15 ´ 5 + 16 ´ 10 + 17 ´ 13 + 18 ´ 7 PM Mean = 1A dividing by 40 40 651 PA 1CA Simplification = 40 (3) = 16,275 PCA 3.3 15 + 16 PA 1A correct values L2 B= 2 = 15,5 PCA 1CA value of B 1M mean concept 16 + 17 PM C= 2 = 16,5PCA 1 CA value of D D = 17PCA (5) 3.4 30 PA 1A 30 grade 9 boys L2 P= 40 PA = 0,75 PCA 1A no. of boys 40 1CA decimal (3) 3.5 The grade 9 boys are too old for their grade. 2J reason L4 PPJ OR Social: Need recognition / low self- esteem / identity crisis. OR Economic: To gain favours from others. PP J Unemployment in the community, come from poor homes PP J OR 41

Educational: They are frustrated by their lack of progress. PP J OR Environmental factors/ emotional factors OR Contextual factors/ No parental control/Peer pressure PP J OR (2) Violent community / child headed family/gang related PP J OR Any other reasonable justification PP J Question 4 Q Solution/s Explanation L 4.1 4üüA 2A correct answer L2 (2) 4.2 Range is the difference between the highest/maximum value 2A correct definition L2 and the lowes/minimum value in a data set. üüA (2) 4.3 25%üüA 2A percentage L2 (2) 4.4 üA L3 #$ 1A 75% Number of learners = %&& ´ 20üMA 1MA multiplying by 20 = 15üCA 1CA simplification (3) 4.5 L4 It means that 50% of learners scored 22 marks and belowüüO 2O explanation OR It means that 50% of learners scored 22 marks and aboveüüO 2O explanation (2) 42

4. EXAMINATION GUIDANCE PAPER 1 Weighting oftopics Finance 60% (±5) Data Handling 35% (±5) Probability 5% Including Growth Charts (CAPS page 65) assesses application of measures of spread in data handling. Structure and scope Question 1:30 marks ± 5 marks of contentand/or skills Level 1 questions from Finance and Data Handling Question 2 Finance Question 3 Data Handling Question 4 Integrated context on Finance and Data Handling Including Growth Charts (CAPS page 65) assesses application of measures of spread in data handling. Question 5 Finance, data handling or integrated question Probability will be examined in thecontext of one or more of the other questions. Each question can contain more than one context. N.B Each paper may have 4 or 5 questions Topics % 150 marks Finance 60% 90 Level 1: Knowing 30% (±45 marks) Taxonomy levels Data 35% 53 Level 2: Applying routine proceduresin 30% (±45 marks) handling familiar contexts PAPER 1 Probability 5% 7 Level 3: Applying multi-step 20% (±30 marks) procedures in a variety of contexts 100% 150 marks Level 4: Reasoning and reflecting 20% (±30 marks) 43

Time and mark allocation Paper 1 Duration Marks 3 hours 150 Marks Time management for Examination preparation: If you have 100 hours to prepare for the examination, the following can be used as a guide on how to use your hours: Application Topics Number of hours Finance 60 Data handling 35 Probability 5 Order of the questions in the question paper Each paper may have 4 or 5 questions. Paper 1: QUESTION 1 (30 marks ± 5 marks ONLY taxonomy Level 1.) Short context – mixed questions(Finance and Data Handling.) QUESTION 2 – Finance QUESTION 3 – Data Handling QUESTION 4 – Finance and Data Handling QUESTION 5 – Finance, Data Handling or integrated Probability will be integrated in all five questions, where it is appropriate. GUIDANCE Set a goal (marks you would like to see on your Matric Certificate) at the beginning of the term, If for example your aim is to achieve 60% for Mathematical Literacy. One way of getting it is as follows: Paper 1: 90 marks out of a possible 150 Paper 2: 90 out of a possible 150 A total of 180 out of 300 = 60% 44

5.GENERAL EXAMINATION TIPS 1. Study the matric timetable. Know when you are going to write the papers you have registered for. There are sometimes two exams on one day so you will have to be super sharp and alert. Be sure to check the final timetable in case there are any changes. 2. There are less than 123 days to the start of the final exams. This includes all weekends and holidays. Start today and work every day. Set targets for achievement. 3. Do not miss one day of studying between now and your exams. Work at least two to three hours per day. Keep healthy and alert. 4. Reading is a hot skill. Reading will change your life. Read at least 1000 words every day. Read everything you can get your hands on. Read accurately and quickly. 5. Writing is power, but it requires practice. We are all judged, every day, on our writing. We can inspire, impress, persuade, congratulate and express love in writing. Write at least 400 words every day carefully, accurately and beautifully. 6. Resources are an essential student companion. Work systematically through your question papers and Self Study Guide. Don’t wait for your face-to-face classes or broadcasts to explain it all. Look at what you have to cover for the subject and plan accordingly. 7. Your BMI can help you in matric. Your Body mass Index (BMI) is an indication of how healthy you are. Calculate your BMI and then exercise and eat healthy throughout the year to keep an optimum BMI. 8. Academic work requires concentration and focus. Every day you should be engaged in intensive, focused, individual academic work. Turn off iPods, music centres, the TV, the cell phone and have an intensive and rewarding academic work out every day. Except of course if you are using it to access the resources. Be diligent and don’t be tempted to watch or access non – academic material. Technology is a fabulous platform to learn and prepare for the examinations but it can also be a deterrent if you are not focused and dedicated. Build your brain cells and be the envy of all your friends. 9. Good vibes are good for success. Surround yourself with positive people who want you to succeed. Your family and friends will be important ibn supporting you in the next 123 days. Be grateful for their support. 10. Matric success requires Planning and hard work. Start planning and working today. Read every day. Write and calculate every day. Stick to your year plan. 45

6. References 1 NSC Mathematical Literacy, DBE Nov Exam P1, 2008. 2 NSC Mathematical Literacy, DBE Nov Exam P1, 2020. 3 NSC Mathematical Literacy, DBE Nov Exam P2, 2014. 4 NSC Mathematical Literacy, Free State June P1, 2017. 5 NSC Mathematical Literacy, Free State June P1, 2021. 6 NSC Mathematical Literacy, Free State March Test, 2017. 7 NSC Mathematical Literacy, Free State Preparatory exam P2, 2016. 8 NSC Mathematical Literacy, GP (10601) Preparatory Exam P1, 2019. 9 NSC Mathematical Literacy, KZN Preparatory Exam P1, 2017. 10 The Answer Series, Mathematical Literacy, Grade 12. 46

7. Acknowledgements The Mathematical Literacy Second Chance Self Study Guide Booklet was developed by the following Subject Specialist: • Ms Arden Ellie (Eastern Cape Education Department) • Ms Thembeka Nethe (Free State Education Department) • Mr Nzimeni Koba (Free State Education Department) • Mr Peter Kekana (Gauteng Education Department) • Mrs Zandile Mdiniso (KwaZulu – Natal Education Department) • Ms Mary Sebela (Limpopo Education Department) • Mr Kwazinkosi Gwate (Northern Cape Education Department) The Department of Basic Education (DBE) gratefully acknowledges these officials for giving up their valuable time, families and knowledge to develop this resource for the children of our country. It was also reviewed by the following Subject Specialist: • Ms Luleka Nombombo (Eastern Cape Education Department) • Dr Reinette van der Merwe ((Free State Education Department) • Ms Nikiwe Zulu (Gauteng Education Department) • Ms Lorraine Govender (KwaZulu – Natal Education Department) • Ms Saloshni Pillai (KwaZulu – Natal Education Department) A special mention must be made to Ms Masirheni Gladys Nkwinika, the DBE curriculum specialist who, in addition to her contribution to the development of the booklet, co-ordinated and finalised the process. The development of the Study Guide was managed and coordinated by Ms Cheryl Weston and Dr Sandy Malapile 47

ISBN : 978-1-4315-3508-8 he High Enrolment Self Study Guide Series basic education This publication is not for sale. a )) Bote edvceton © Copyright Department of Basic Education RS REPUBLIC OF SOUTH AFRICA www.education.gov.za | Call Centre 0800 202 993