1. KS3 Mean, Mode, Range Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 12 th October 2013

2. Averages There are different averages: some are more meaningful than others depending on the context. What is the average number of ears in the world human population? The mode (the “modal average”) The median The mean The mode represents the most common value. Modal number of ears: 2 ? Median number of ears: 2 ? ? The median represents the middle value. ? The mean takes into account all values. We add up the values and divide by the number of values. Mean number of ears: 1.99999 ?

3. Averages The mode (the “modal average”) The median The mean The mode tends to be a good average when we want to give an indication of the value that is most common. Median is often good because it makes it easier to tell whether a value is in the top 50% or the bottom 50%. It’s also less sensitive to extreme values. The mean is the best average to use if we want to take all the values into account. There are different averages: some are more meaningful than others depending on the context. Salaries of people in the room: £13,000 £18,000 £24,000 £25,500 £26,000 £32,000 £45,000 £1,200,000 What would the best average be here?

4. Averages Copy these numbers down, and work out the mean, mode and median. 10, 13, 15, 16, 17, 17, 20 The mode (the “modal average”) The median The mean 10 + 13 + 15 + 16 + 17 + 17 + 20 7 = 15.43 ? 16 ? 17 ?

5. Averages – Round 2! Copy these numbers down, and work out the mean, mode and median. 13, 13, 17, 20 The mode (the “modal average”) The median The mean 15 ? 13 ? The range 15.75 7 ? ? The range is the difference between the smallest and largest number. When there’s two items in the middle, we use the value in between: i.e. add them and divide by 2.

6. In pairs, see how many of these puzzles you can work out… The mean average of Dr Frost and Sebastian’s age is 19.5. If Sebastian is 13, how old is Dr Frost? Answer: 26 ? If the range of two numbers is 6 and the their mean is 15, what are the two numbers? Answer: 12 and 18 ? The mode of four numbers is 5. The median is 6.5 and the mean is 7. What is the range? Answer: 7 (The numbers are 5, 5, 6, 12) ? The mean of the four numbers is 8. What is the missing number? 345? Answer: 20 ? 1 Puzzles involving the mean 2 34

7. Worksheet provided! Exercises

8. KS3 Mean of Frequency Tables Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 22 nd November 2013

9. Age of Dog1011121314 Frequency34761 The “frequency” tells us how “frequent” the age of 10 is, i.e. how many times it appears. ? Mean of Frequency Tables Bro Tip: Imagine if we actually listed out the values – how would we find the mean?

10. Cost£1.50£1.65£1.70£1.80£2.00 Frequency1202152 Mean cost of beefburger horseburger: = = £1.70 £83.20 49 ? Your Go... Weight2kg3kg4kg5kg6kg Frequency40873 Mean weight of cats: = = 4.23kg 93 22 ?

11. Time (secs)Frequency Mean of Grouped Data A number of members of 8IW are running in a race. Their times were as follows ? Why is it an estimate? Because we don’t know the exact times within each group. ?

12. Age of rock (years)Frequency Test Your Understanding Weight of horse (kg) Frequency ? ?

13. Exercises (Provided on printed sheet) Height (nearest cm)6cm7cm8cm9cm10cm Frequency381241 Weight10-16kg16-20kg20-30kg30kg-32kg Frequency7341 Value£0-£1000£1 000-5 000£5 000-£20 000£20 000-£100 000 Frequency102561 Time (minutes)35-4040-4242-4848-60 Frequency5152010 ? ? ? ? ? ? 1 2 3 4 5 6

14. Exercises ? ? 6 7