Mathematical Literacy Level 3 Module 17

Mathematical Literacy NQF 3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Represent and interpret data Module 17 Downloaded from hlayiso.com Maths Lit NQF Level 3

Overview 17.1 Measures of central tendency and spread 17.2 Read and represent data in graphs and tables 17.3 Choosing the appropriate representation Downloaded from hlayiso.com Maths Lit NQF Level 3

Measures of central tendency and Unit 17.1 spread Data sets In statistics, the lists of data that we have collected, are called data sets. • We need to interpret the data by summarising and representing the data. ” • The first step in the process is to find the measures of central tendency. Downloaded from hlayiso.com Maths Lit NQF Level 3

Measures of central tendency and Unit 17.1 spread Central tendency Central tendency refers to how the numbers are grouped or spread around the average value that gives the position of the centre of the data. ” • The three different measures of central tendency tell us different things about a data set. • Each of these measures of central tendency can be defined by the way in which they are calculated. Downloaded from hlayiso.com Maths Lit NQF Level 3

Measures of central tendency and Unit 17.1 spread • These measures are: Mean Median Mode Note: Do not get confused with the meaning of the word average. It can refer to all 3 measures of central tendency. The calculated average refers to the mean. Downloaded from hlayiso.com Maths Lit NQF Level 3

Measures of central tendency and Unit 17.2 spread Downloaded from hlayiso.com Maths Lit NQF Level 3

The advantages and disadvantages of using measures of central tendency and spread Unit 17.1 Advantages Disadvantages • useful in describing measured • does not tell us the number of high mean values or low values. • does not show data distribution • gives us the middle value of a • does not use the actual values of the data set data - uses their positions in the • tells about the data differs in the ordered data median bottom half and the top half of the data set • not affected by very high or very low values. Downloaded from hlayiso.com Maths Lit NQF Level 3

The advantages and disadvantages of using the measures of central tendency and spread Unit 17.1 Advantages Disadvantages • on a bar graph comparing the • Not all data has a mode number of items in different categories, the mode is easy to mode identify as the highest bar • useful for categorised data e.g. shoes sizes • Not all data sets have a mode. • Some data sets have more than one mode. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 17.2 page 321 Unit 17.1 Which averages are referred to in the following article and how were they calculated? A research survey was carried out in a supermarket to see at what times people prefer to do their grocery shopping. Most people prefer to shop between 4 p.m. and 7 p.m. in the evenings during the week or between 9 a.m. and 12 p.m. on Saturdays and Sundays. The number of people visiting the mall per day over one month ranged from 800 to 3 890 people. The average number of people visiting the mall each day was 2 890 people, while the median was 2 011. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 17.2 page 321 continued ... Unit 17.1 • There were two kinds of data collected: the times when people arrived and the numbers of people. • The data for the number of people arriving at the shopping mall has been arranged in the time intervals in which people shop. The mode is the most popular shopping time. • The word ‘most’, is a clue to check if this gives you the mode of the data. • The mean of the number of people coming to the mall each day was calculated and given as the average. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 17.2 page 321 continued ... Unit 17.1 • The median number of people is also given. • The median is lower than the mean. This shows us that data is not distributed uniformly. • On half of the days, less than 2 011 people visited the mall and on half of the days more than 2 011 people came to the mall. • The mean is higher than the median because there were a few days when the number of people was very high. Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 17.1 Unit 17.1 Complete Exercise 17.1 on page 324 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Read and represent data in graphs and tables Unit 17.2 Data is usually represented in two ways, using : Graphs Tables Deciding which graph to use is determined by the type of data that is being represented, namely: • Discrete data – values are whole numbers or names of things. • Continuous data – values representing measurements, include all number values. Downloaded from hlayiso.com Maths Lit NQF Level 3

Read and represent data in graphs and tables Unit 17.2 Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 17.2 Unit 17.2 Complete Exercise 17.2 on page 331 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Choosing the appropriate representation Unit 17.3 • Choose the method of displaying data according to the kind of data and what you want the focus to be. Bar graphs Bar graphs are convenient when we want to compare the quantities of things in different categories. Downloaded from hlayiso.com Maths Lit NQF Level 3

Choosing the appropriate representation. Unit 17.3 • Choose the method of displaying data according to the kind of data and what you want the focus to be. Pie charts Pie charts show us the relative percentages of items as proportions of a whole, but they often do not show the actual numbers of things. Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 17.3 Unit 17.3 Complete Exercise 17.3 on page 333 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

VIDEO: Applications in the workplace Downloaded from hlayiso.com Maths Lit NQF Level 3

Module assessment Module 17 Complete Module assessment on page 336 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

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