Mean, median, mode, range

The “mean” is the “average” you’re used to, where you add up all the numbers and then divide by the number of numbers.

The “median” is the “middle” value in the list of numbers.

To find the median, your numbers have to be listed in numerical order from smallest to largest, so you may have to rewrite your list before you can find the median.

The “mode” is the value that occurs most often. If no number in the list is repeated, then there is no mode for the list.

Range is the difference between the highest and lowest value

Example1

Find the mean, median, mode, and range for the following list of values:

12, 18, 12, 14, 12, 16, 14, 21, 13

(i) The mean is the usual average, so I’ll add and then divide:

(12 + 18 + 12 + 14 + 12 + 19 + 14 + 21 + 13) ÷ 9 = 15

Note that the mean, in this case, isn’t a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.

(ii) The median is the middle value, so first I’ll have to rewrite the list in numerical order:

12, 12, 12, 13, 14, 14, 18, 19, 21

There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

12, 12, 12, 13, 14, 14, 18, 19, 21

So the median is 14.

(ii) The mode is the number that is repeated more often than any other, so 12 is the mode.

The largest value in the list is 21, and the smallest is 12, so the range is 21 – 12 = 9.

mean: 15
median: 14
mode: 12
range: 9

Note: The formula for the place to find the median is “([the number of data points] + 1) ÷ 2”, but you don’t have to use this formula. You can just count in from both ends of the list until you meet in the middle, if you prefer, especially if your list is short. Either way will work.

Example 2

Find the median, mean, mode and range of the following numbers: 0, 6, 2, 5, 1, 9, 5, 1, 6, 5,

(i) Arrange the number in increasing order: 0, 1, 1, 2, 5, 5, 5, 6, 6, 9

The median is the middle number = (5 + 5)/2 = 5

(ii) The mean = (0 + 6 + 2 + 5 + 1 + 9 + 5 + 1 + 6 + 5)/10 = 4

(iii) Mode is the most common number = 5

(iv) Range is the difference between highest and lowest numbers = 9 – 0 = 9

For addition exercise and answers  download PDF

Mean, mode, median, range – upper primary.docx

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