Math Chapter 10.2

Using Statistics

In a real situation, you need to decide which one to use.

If you want to measure how spread out a set of measurements is, the range is the most useful statistic.

If you want to find a representative measurement, you need an average. Should it be the mode, the median, or the mean? That depends on the particular situation.

Here is a summary to help you decide which average to choose:

• Choose the mode if you want to know which is the most commonly occurring number.
• The median is the middle value, when the data values are put in order. Half the numbers are greater than the median and half of the numbers are less than the median.
• The mean depends on every value. If you change one number you change the mean. 

 Worked Example:

Here are the ages, in years, of the players in a football team.
Work out the average age. Give a reason for your choice of average.

16

17

18

18

19

20

20

21

21

32

41

Answer:

> The mode is not a good choice.
   --->   There are 3 modes. Each has a frequency of only 2.

> The mean will be affected by the two oldest people.
  ---> They are much older and will distort the value. In fact the mean is 22.1 and 9 people are younger than this; only 2 are older.

> The median is 20 and this is the best average to use in this case.
  ---> 5 players are younger than the median and 5 are older.