10.2 Using 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 to spread out a set of measurements is, the range is the most statistic.

If you want to find a representative measurements, you need an average. Should it be the mode, 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 occuring number.
• The Median is the middle value, when the data values are put in order. Half the number 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 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 reasonfor your chioce of average.

16

17

18

18

19

20

20

21

21

32

41

• The mode id not a good choice

            There are three modes. Each has a frecuency of only 2

• The mean will be affected by the two oldest people

             They are much older and will dostort the value. In fact, the mean is 22.1 and nine people are      younger than this; only two are older

• The median is 20 and this is the best average to use in this case

            Five players are younger than the median and five are older  

10.1 Calculating Statics

You can use statistics to summarise sets of data.

You can also use to compare different sets of data.

You should already be able to calculate three different averages: 

The Mode, The Median, The Mean

Remember that the range is not an average. It measures how spread out a set of value or number is. For a large set od data, it is not practical to list every number separetly. Instead, you can record the data in frequency table.

The Mode is the most common value or number.

The Median is the middle value, when they are listed in order.

The Mean is the sum of all the values divided by the number of values.

The Range is the largest value minus the smallest.

WORKED EXAMPLE:

Number of Beads	25	30	35	40	45	50
Frequency	34	48	61	30	15	12

The tables shows the number of beads on 200 necklaces.

a) Find the mode

b) Find the mean

c) Find the range

ANSWER:

a) The Mode is 35   

    --> The mode is the number with the highest frequency

b) 6900 / 200 = 34.5 

   --> (25 x 34 + 30 x 48 + 35 x 61 + 40 x 30 + 45 x 15 + 50 x 12 ) divided by the sum of all frequencies.

          This is the middle of all the possible number of beads.

c) 50 - 25 = 25

  --> This is the difference between the largest and the smallest number of beads