Mathematical Literacy Level 2 Module 16

Mathematical Literacy NQF 2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Represent and interpret data Module 16 Downloaded from hlayiso.com Maths Lit NQF Level 2

Overview 16.1 Summarising data 16.2 Representing data Downloaded from hlayiso.com Maths Lit NQF Level 2

Summarising data Unit 16.1 • To summarise data, we want a number that best represents all the data in a set of scores. • Numbers that describe the average data value we call ‘measures of central tendency’ Mean Median Mode Downloaded from hlayiso.com Maths Lit NQF Level 2

Calculating the mean Unit 16.1 • The mean (or the arithmetic mean) is a single value that represents an average of all the values in a data set. • We add all the raw scores and divide by the number of scores in the data set to calculate the mean. Arithmetic mean = Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 16.1 page 297 Unit 16.1 Your marks are 62%, 86% and 70% for three tests. What is your mean score? • Step 1: Add the three marks: 62 + 86 + 70 = 218 • Step 2: Divide the total by the number of tests: 218 ÷ 3 = 72,66… • Step 3: Round off your answer and make sure you include the units: 72,7 % Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 16.1 Unit 16.1 Complete Exercise 16.1 on page 279 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Calculating the median Unit 16.1 • The median is the value in the position that splits the set of data into two equal lists of values. • Arrange all the scores (numbers) in ascending order. Then find the middle number. Median = arrange scores in ascending order = ahe middle score is the median Downloaded from hlayiso.com Maths Lit NQF Level 2

Calculating the median continued ... Unit 16.1 If you get 62%, 86%, 50%, 45% and 70% for five tests, find the median. Step 1: Sort the marks into order from lowest to highest: 45%; 50%; 62%; 70%; 86% Step 2: Look for the middle number in the list: 62% The median score is 62%. Downloaded from hlayiso.com Maths Lit NQF Level 2

Calculating the median continued ... Unit 16.1 If there is an even number of scores: If you get 62%, 86%, 79% and 70% for four tests. Step 1: Arrange the scores in order: 62%, 70%, 79%, 86% Step 2: Look for the middle two values: 70%, 79% Step 3: Calculate the average (or midpoint) between these values: = 70 + 79 = 149. 149 ÷ 2 = 74,5 The median is 74,5 Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 16.2 Unit 16.1 Complete Exercise 16.2 on page 299 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Calculating the mode Unit 16.1 • The mode is the value that appears the most number of times in the set of data. • Not all data has a mode value and not all data has only one mode value. Mode = The score/s with the highest frequency Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 16.3 Unit 16.1 Complete Exercise 16.3 on page 301 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Which measure of central tendency Unit 16.1 is more useful? • The mode is useful when data are in discrete categories e.g. if we look at shoe sizes, a mode of 7 would mean more than a mean of 6,75 or a median of 6. • When working with continuous measurement data such as volume, height, length, distance or mass, the mean is useful. • When data is clustered around the mean value, the mean is a good value to use as the average of the data set. • When data is too spread out, the mean is less representative of the data. Downloaded from hlayiso.com Maths Lit NQF Level 2

Measures of spread (dispersion) Unit 16.1 • Measures of spread or dispersion give us information about how spread out the data set is. • The simplest measure of dispersion of data is called the range. • The range of a set of data is the difference between the highest and lowest values in the data set. • The word range can be used in different ways e.g. Maths Literacy marks range from 60% to 90% or there are a wide range of cars these days. Downloaded from hlayiso.com Maths Lit NQF Level 2

Calculating the range Unit 16.1 Range = highest – lowest score Downloaded from hlayiso.com Maths Lit NQF Level 2

Calculating the range Unit 16.1 In a table of class height, the highest is 1,84m, the lowest 1,71 m. Calculate the range. Range = highest – lowest score = 1,84 – 1,71 = 0,13 m (i.e. a narrow range) Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 16.4 Unit 16.1 Complete Exercise 16.4 on page 304 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Representing data Unit 16.2 • Data can be represented in lists, tables and different types of graphs. Tables Line and Tables Tables and broken line and and bar graphs graphs pie charts histograms • The choice of what type of graph to use is determined by the type of data that it represents. Downloaded from hlayiso.com Maths Lit NQF Level 2

Representing data Unit 16.2 Definition Bar graphs are used for the display of a single category or observation against the frequency of its occurrence. ” Downloaded from hlayiso.com Maths Lit NQF Level 2

Representing data Unit 16.2 Definition Line graphs or straight line graphs are used to display the relationships between two sets of continuous data. ” Downloaded from hlayiso.com Maths Lit NQF Level 2

Representing data Unit 16.2 Definition Broken line graphs show values that have been selected at specific moments. The horizontal axis represents discrete data, while the vertical axis represents continuous data. ” Downloaded from hlayiso.com Maths Lit NQF Level 2

Representing data Unit 16.2 Definition Pie charts are used to display data (usually as a percentage) and each sector or segment represents a portion of the total circle. ” Downloaded from hlayiso.com Maths Lit NQF Level 2

Representing data Unit 16.2 Definition Histograms are used when we represent grouped continuous data i.e. when data is in class intervals. Histograms are similar to bar graphs, but there are no spaces between the ” columns. Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 16.5 Unit 16.2 Complete Exercise 16.5 on page 312 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Has the data been shown correctly? Unit 16.2 • If the wrong type of graph is used the data may be distorted to the viewer. Always check that the data is plotted correctly. Incorrect plotting can also lead to a false interpretation of the data. • Changing the scale of the axis: on a line or bar graph, this results in the values either being too close together or too far from each other, which can distort the representation of the data. Downloaded from hlayiso.com Maths Lit NQF Level 2

Take a look at these two graphs Unit 16.2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Using pictures for representations Unit 16.2 • The size of elements used in a graph affect the way a person perceives the information. 3-D pictures create the illusion that the differences between data are more pronounced than they actually are. • To ask if a graph represents data fairly ask the following: • Is the scale correct? • Has the correct type of graph been used for this type of data? • Are there any seasonal or other variations that would influence the data? • Has a three-dimensional representation been used? If so, is it appropriate and balanced? • Has information on the axes of the graph been changed or left out altogether? Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 16.6 Unit 16.2 Complete Exercise 16.6 on page 319 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 16.7 Unit 16.2 Complete Exercise 16.7 on page 321 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Applications in the workplace Downloaded from hlayiso.com Maths Lit NQF Level 2

Module assessment Module 16 Complete Module assessment on page 324 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

TERMS AND CONDITIONS This PowerPoint Presentation has been developed by Macmillan Education South Africa (Pty) Ltd. All texts, images, videos, animations, audio and vector simulations contained in the slides are property of Macmillan South Africa. Reproducing, reselling and redistributing this material without the written permission of Macmillan South Africa is prohibited. Lecturers are granted permission to: (i) modify the slides by adding and removing content; (ii) print copies of the presentation; and (iii) download and save the slides to a computer or local server. Nothing in this copyright notice constitutes permission to assert or imply that your use of the materials is sponsored or endorsed by Macmillan South Africa. Downloaded from hlayiso.com Maths Lit NQF Level 2