Averages Aim To calculate averages and the range

Averages Aim: To calculate averages and the range.

What is an average? ? 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.

Think… Why would we want to find an average?

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.

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.

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

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

From the following sets of data find the: (a)Mean (b) Mode 10 8 (c) Median 3 4 9 (d) Range 8 7 Mean = 7 Mode = 8 Median = 8 Range = 7 120 122 130 131 130 129 128 132 139 Mean = 129 Mode = 130 Median = 130 Range = 19 27 12 56 23 98 27 28 27 Mean = 37. 25 Mode = 27 Median = 27 Range = 86

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

Here is a frequency table: Shoe size Frequency 3 3 4 5 5 10 6 9 7 8 8 4 Frequency is the number of times something occurs

The Can. MODE you remember is the most what popular the MODE number! means? To find the MODE from a frequency table, it is the number with the highest frequency! Can you see the mode from your frequency table? Shoe size 3 4 5 6 7 8 10 is the highest frequency, so shoe size 5 is the mode Frequency 3 5 10 9 8 4 Look for the biggest number

The you Can Range remember is the biggest what the number Range– the is? 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? The biggest shoe size is 8, the smallest shoe size is 3. Range is 8 – 3 = 5 Shoe size 3 4 5 6 7 8 Look for the biggest and smallest Frequency 3 5 10 9 8 4

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

To find Can The you median the remember median is the middle what of data the value inmedian a when frequency is? the data table, is put to find in order! where the middle of the frequency will be! Shoe size 3 4 5 6 7 8 Frequency 3 5 10 9 8 4 Find the total of the frequency column To find the median, you need to add one to the total of the frequency and divide by two 39 So the median would be the 20 th value in the table Median = size 6

Find the mean, mode median and range of the following tables Shoe Size Frequency 4 3 5 4 6 5 7 2 Height (cm) 156 157 158 Frequency 21 34 42 159 160 37 19 Weight (kg) Frequency 42 1 43 2 44 5 45 5 46 4 47 3