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# What are the 3 averages? Questions on the mean, median and modal values.

The main 3 averages which you need to remember are the mean average, the median average and the modal average (mode).

Finding the mean can be done by working out the total of the numbers and dividing by how many numbers you have.

Finding the median can be worked out by putting the numbers into numerical order and writing down the middle number. Sometimes you will find that there are two numbers in the middle, so you need to work out the middle value of these two numbers.

Finding the mode can be done by finding the number which is most frequent. If two numbers occur more than the others then write both of these answers down (bi-modal). If there isn’t a number which is more frequent than the others then there isn’t a mode (write down no mode).

Example

12 athletes take part in 100m race. Here are their times to the nearest tenth of a second:

10.4, 10.2, 11.4, 11.9, 10.4, 10.1, 10.9, 11.3, 11.3, 10.4, 12.1, 11.0

Work out the mean, median and modal values.

Mean = (10.4 + 10.2 + 11.4 + 11.9 + 10.4 + 10.1 + 10.9 + 11.3 + 11.3 + 10.4 + 12.1 + 11.0) ÷ 12 = 10.95

Median

10.1, 10.2, 10.4, 10.4, 10.4, 10.9, 11.0, 11.3, 11.3, 11.4, 11.9, 12.1

10.9 and 11.0 are in the middle, so the median average is 10.95.

Mode

10.4 as 10.4 is the most frequent number.

Example 2

The heights of 5 people are recorded as follows:

Work out the mean, median and modal values.

1.72m, 1.85m, 1.64m, 1.73m, 1.9m

Work out the mean, median and mode.

Mean = (1.72 + 1.85 + 1.64 + 1.73 + 1.9) ÷ 5 = 1.77m

Median = 1.64, 1.72, 1.73, 1.85, 1.9 = 1.73m

No mode

Example 3

Adam, Ben, Charlie, Derek and Edward take a maths test. The mean average of all their marks is 64%. What is Edwards score, if Adam scored 57%, Ben scored 73%, Charlie scored (80%) and Derek scored 34%?

If you multiply the mean average by the amount of people who took the test, then this will give you the total score:

64 × 5 = 320

So 320% is the total score of Adam, Ben, Charlie, Derek and Edward.

Next, the total score of Adam, Ben, Charlie and Derek is:

57 + 73 + 80 + 34 = 244

All you need to do next is work out the difference between 320% and 244%

320 – 244 = 76%

So Edward scored 76%.

There are other types of averages but these are for students studying math at a higher level.