1. Using grouped frequency tables – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 Toolbox Mean from grouped data Continuous data Choosing groups Mean of continuous data Contents

2. Using grouped frequency tables – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 For large amounts of data use a grouped frequency table. Between 5 and 10 groups (or classes) is usually most suitable. Show classes for continuous data using “less than” < or “less than or equal to” ≤. Toolbox MenuBackForward To estimate the mean from a grouped frequency table use the mid-interval value for each group. Multiply the mid-interval value by the frequency. Add the results. Divide that answer by the total frequency. Round the answer for a suitable estimate. The modal class has the highest frequency.

3. Using grouped frequency tables – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 Ronny goes to the City of London. He records the number of floors in the buildings near Liverpool Street Station. 1.Make a tally chart using the groups 1–5, 6–10 and so on. What is the modal class? 2.Calculate the mean number of floors for the buildings. Mean from grouped data Mean number of floors = 248 ÷21 = 11.8095... = 12 to the nearest whole number. MenuToolboxBackForwardAnswer 1 Answer 2 Do a similar survey of buildings in your nearest big town or city. More Number of floors Mid-interval value FrequencyMid-interval value × frequency 1–5339 6–108540 11–1513791 16–20186108 TOTALS21248 The modal class is 11–15 floors. Number of floors Tally 1–51–5///3 6–10//// /5 11–15//// //7 16–20//// /6 Total21

4. Using grouped frequency tables – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 a)Foot length can take any value. It is continuous. b)Shoe sizes can only take whole numbers (or halves in British sizes). It is discrete. c)This must be a whole number. It is discrete. d)This could be any weight. It is continuous. e)This must be a whole number. It is discrete. Are the following data discrete or continuous? a)Foot length. b)Shoe size. c)The number of coins in my pocket. d)The weight of coins in my pocket. e)The number of heads obtained when a coin is tossed 100 times. Continuous data MenuToolboxBackForwardAnswer

5. Using grouped frequency tables – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 Here are two sets of continuous data. Choosing groups MenuToolboxBackForwardAnswer The range for firework times (t) is from 10 s to 35 s. 5 groups of 5 seconds is best: 10 ≤ t <15, 15 ≤ t < 20 etc. The range for the 100 m times (t) is 13.1 s to 21 s. 5 groups of 2 seconds is best: 12 ≤ t <14, 14 ≤ t <16 etc. 1.What intervals would you use for grouping each set of data? Remember that between 5 and 10 is usually suitable for the number of groups.

6. Using grouped frequency tables – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 Temperature °C (T)TallyFrequency 10 ≤ T< 12 12 ≤ T < 14 14 ≤ T < 16 16 ≤ T < 18 18 ≤ T < 20 The maximum temperature, in °C, is recorded in Auckland for each day in June and shown on the right. 1.Copy and complete this tally chart and frequency table. Mean of continuous data MenuToolboxBackForwardCont/dAnswer Temperature °C (T)TallyFrequency 10 ≤ T< 12 /// 3 12 ≤ T < 14 //// // 7 14 ≤ T < 16 //// //// // 12 16 ≤ T < 18 ////5 18 ≤ T < 20 /// 3

7. Using grouped frequency tables – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 Below is a table ready that can be used to work out an estimate for the mean temperature for June. 11,13,15,17 and 19. 1.What numbers should you use for the mid-interval values? 2.Now complete the table and calculate your estimate for the mean temperature. MenuToolboxBackAnswer 1 Answer 2 Temperature °C T Mid-interval value M Frequency F M × F 10 ≤ T < 12 3 12 ≤ T < 14 7 14 ≤ T < 16 12 16 ≤ T < 18 5 18 ≤ T < 20 3 Totals The estimate for the mean is 422 ÷ 30 = 14.066… = 14.1 °C to 1 d.p. Mean of continuous data Temperature °C T Mid-interval value M Frequency F M × F 10 ≤ T < 12 339 12 ≤ T < 14 13791 14 ≤ T < 16 1512180 16 ≤ T < 18 17585 18 ≤ T < 20 19357 Totals30422

8. Using grouped frequency tables – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 Editable Teacher Template MenuToolboxBackForwardAnswer 1More Information 1.Task – fixed 2.Task – appears Answer 1 Answer 2 More Answer 2