1. Averages Aim: To calculate averages and the range.

2. The average value is a number that is typical for a set of figures. The average is like the middle point of the numbers. Finding the average helps you do calculations and also makes it possible to compare sets of numbers. What is an average??

3. Think… Why would we want to find an average?

4. Mode The mode is the value in the data that occurs the most. For example in a list of peoples' favourite films the mode would be the most popular choice - the one with most votes. Example Find the mode of 6, 4, 6, 5, 3, 7, 6 You can see that 6 is the most common number in the list. There are three of them. We say that 6 is the mode of this set of data.

5. Median The median is the middle value when the data is arranged in size order. Example Find the median of these numbers 6, 4, 6, 5, 3 First put the numbers in order. This makes it easier to find the median 3, 4, 5, 6, 6, You can now see that 5 is the middle number. It is half way along the list. So the median value of this set of data is 5.

6. Mean The mean average shows us what would happen if there were equal shares. (everybody got the same!) To calculate the mean: mean value = total amount ÷ number of figures Example Calculate the mean of 16, 13, 21 and 14. The total of these numbers is 16 + 13 + 21 + 14 = 64 There are 4 figures, so divide the total by 4, 64 ÷ 4 = 16 So the mean is 16

7. Range The range is a measure of spread. It describes how the data is spread out. To find the range we do: Biggest number – Smallest number Example What is the range of 2 5 9 6 5 10 2 11 Biggest number = 10 Smallest number = 2 Range = 10 – 2 = 8

8. From the following sets of data find the: (a)Mean(b) Mode(c) Median(d) Range 10 8 3 4 9 8 7 120122130131130129128132139 2712562398272827 Mean = 7 Mode = 8 Median = 8 Range = 7 Mean = 129 Mode = 130 Median = 130 Range = 19 Mean = 37.25 Mode = 27 Median = 27 Range = 86

9. Averages from a frequency table Aim: To be able to find the four types of average from a frequency table

10. Shoe sizeFrequency 33 45 510 69 78 84 Here is a frequency table: Frequency is the number of times something occurs

11. Can you remember what the MODE means?The MODE is the most popular number! To find the MODE from a frequency table, it is the number with the highest frequency! Shoe sizeFrequency 33 45 510 69 78 84 Can you see the mode from your frequency table? Look for the biggest number 10 is the highest frequency, so shoe size 5 is the mode

12. Can you remember what the Range is?The Range is the biggest number – the smallest number To find the range in a frequency table, you subtract the biggest piece of data from the smallest Can you see the range from your frequency table? Shoe sizeFrequency 33 45 510 69 78 84 Look for the biggest and smallest The biggest shoe size is 8, the smallest shoe size is 3. Range is 8 – 3 = 5

13. Can you remember what the mean is?mean value = total amount ÷ number of figures To find the mean from a frequency table to need to follow the steps below: Shoe sizeFrequencyShoe size x frequency 33 45 510 69 78 84 Mean = (total of shoe size x frequency) ÷ (Total frequency) Add an extra column 3 x 3 = 9 4 x 5 = 20 5 x 10 = 50 6 x 9 = 54 7 x 8 = 56 8 x 4 = 32 Add an extra row to show the total of that column 221 39 Mean = 221 ÷ 39 =5.7

14. Can you remember what the median is?The median is the middle value when the data is put in order!To find the median of data in a frequency table, to find where the middle of the frequency will be! Shoe sizeFrequency 33 45 510 69 78 84 Find the total of the frequency column 39 To find the median, you need to add one to the total of the frequency and divide by two So the median would be the 20 th value in the table Median = size 6

15. Find the mean, mode median and range of the following tables Shoe SizeFrequency 43 54 65 72 Height (cm)Frequency 15621 15734 15842 15937 16019 Weight (kg) Frequency 421 432 445 455 464 473