Back to Unit 11

Notes on Measures of Central Tendency

Measures of Central Tendency enable us to evaluate the usefulness of data.  There are four main measures that we use:  Mean, Median, Mode and Range.

It is recommended that you sort all your data first (from least to greatest)

Mean: The numerical average of a set of numerical data.

To calculate: Add up all the data and divide by the amount of data you have.

Example: Here is a set of race times for the 50 meter Freestyle race:      25 seconds, 28 seconds, 23 seconds, 26 seconds and 23 seconds.

Step 1: put them in order:  23

23

25

26

28

Step 2: add them up:       125

Step 3: divide them by the amount of data – I have five values, so divide by 5.

The mean is 25 seconds

Mode: This is the number that is given most often.  In the case of the data above the mode is 23, It is given twice while all the rest are only given once.  You can have more that one mode and you may not have any mode.

Median:  This is the middle number in a set of data if you have an odd amount of values, otherwise it is the average of the two middle numbers.

In the data above 25 is the median because it is the middle number.

Suppose I have six values instead:

23

23

24

25

26

28

I would calculate the average of the two middle numbers: 24 + 25 = 49

So the median would be 49.5 seconds

Range: This is the difference between the lowest and highest values.  Subtract the least value from the greatest value. 28-23=5  The range in this set of data is 5 seconds.

Finding the missing numerical measure in a set of data is easy using logic.

Suppose you want to find one value in a set of data and you have the mean or the average.  Example: You have 5 values and the mean is 25.  Three of the values are 16, 32, 25 and the mode is 32.  Can you find the missing two numbers?

Well you know that one of them must be 32, because it is repeated more than the other numbers. (It is the mode).  So now you know 4 out of five of the pieces of data.  Add them up. 16 + 32 + 32 + 25 = 105

What would the total be for all five values if the mean is 25?  Multiply 5 times 25 to get its total.  The total would be 125.

Now to find the last missing number subtract 125-105=20.

Check if your calculation is correct: 16 + 32 + 32 +25 + 20 = 125