1. DO YOU KNOW WHAT I MEAN? Aim: To be able to find the mean and mode from a frequency table. All: Will be able to read values from a frequency table. Most: Will be able to find the mean. Some: Will be able to comment on the mean.

2. 27, 27, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 30, 30, 31, 31, 32 Frequency Tables Convenient Hold a large amount of data Easy to use to find averages Class Size 272829303132 f243521 Here is some data on class sizes in a school. Data placed in a frequency table

3. Mean x is variable or the data collected e.g. shoe size, weight, height etc f is the frequency

4. Class Size x 272829303132TOTALS f243521 fxfx Original data in list form: 27, 27, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 30, 30, 31, 31, 32 Frequency Tables Calculating the mean from the frequency table. 54 11287 15062 32 (2 x 27 + 4 x 28 + 3 x 29 + 5 x 30 + 2 x 31 + 1 x 32) 17 Mean = = 497/17 = 29.2 Or if entered directly into a calculator. 17 497

5. Your Turn Page 220 Ex 13B HOMEWORK: To get a broadsheet and a tabloid newspaper. E.g. Broadsheet: The Times, The Independent E.g. Tabloid: The Star, The Sun, Daily Mirror

6. Four Averages Aim: To be able to find the mean, median, mode and range from a frequency table. All will be able to find the mode. Most will be able to find the range and mean. Some will be able to find the median For the exam in 13 days!

7. Definitions Mode is Range is Median is

8. Recap the mean Size x 681012141618 f 13741032 fxfx

9. Izzy wizzy lets get busy Page 206 Ex 11F Q1, 2, 3

10. Grouped Data ScoreFreq 21 – 307 31 – 4012 41 – 5015 51 – 608 Total42 Because we do not know what the exact mark for each pupil was we have to assume that each pupil obtained the middle mark in each group. E.g. in the group 31 – 40, we assume that each of the 12 pupils obtained 35.5 marks

11. Grouped Data Part II ScoreFreqMid PointCalculation (f x mp) 21 – 307 31 – 4012 41 – 5015 51 – 608 Total42 (21+30)/2=25.5 (31+40)/2=35.5 (41+50)/2=45.5 (51+60)/2=55.5 7x25.5= 178.5 12x35.5= 426 15x45.5= 682.5 8x55.5= 444 1731 To work out the mid points we add the upper and lower group limits and divide by 2. To work out the total for each group we then multiply the mid point by the frequency.

12. Estimated Mean mp is the midpoint f is the frequency

13. The Last Step! ScoreFreqMid PointCalculation (f x mp) 21 – 307 31 – 4012 41 – 5015 51 – 608 Total42 (21+30)/2=25.5 (31+40)/2=35.5 (41+50)/2=45.5 (51+60)/2=55.5 7x25.5= 178.5 12x35.5= 426 15x45.5= 682.5 8x55.5= 444 1731 To find the estimated mean;

14. Original data in list form: 27, 27, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 30, 30, 31, 31, 32 Frequency Tables Finding the mode, median and range from the frequency table. Class Size 272829303132 f243521 Mode = 30 (Highest frequency) Median = 29 (The middle data value) [(17 + 1)/2 = 9 th data value.] Range = 32 – 27 = 5