10.2 Calculating Statistics

Now you can work out several different statistical measures.
In a real situation, you need to decide which one to use.
If you want to measure how spread out a set of measurement 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 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 the numbers are less than the median.
• The mean depends on every value. If you change one number you can change the mean.

Worked example 10.2

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.

• There are three modes(18, 20, 21). Each has a frequency of 2. Therefore, the mode is not a good choice.
• They are much older and will distort the value. In fact the mean is 22.1 and nine people are younger than this, only two are older. The mean will be affected by the two oldest people.
• The median is 20. Five players are younger than the median and five are older. Therefore the median is the best average to use in this case.

Another example..
The number of hours in a week that teenagers spent on the computer are recorded below. Determine the mean, the mode and the median and decide which average is the best to use in this case.

• Mean: (10+11+12+13+14+15+16+16+16+16+16+16) ÷ 12 = 14.3

clearly mean is not the best average to use in this case since more than half of the teenagers whose data are

recorded above spent more than 14.3 hours a week on the computer.

13.2 hours on the computer in a week.

• Mode: The mode of this data is 16 which is the best average to use.

Because most of the teenagers there spent 16 hours a week on the computer. 

• Median: the middle value of the data above is (15 + 16) ÷ 2 = 15.5 

This could be the a good average to use but mode is the best average to use in this case.

-pristina-