Mean, mode and median

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Measures of average in grouped and continuous data

The mean

We already know how to find the mean from a frequency table. Finding the mean for grouped or continuous data is very similar.

The grouped frequency table shows the number of CDs bought by a class of children in the past year.

 

Number of CDs	Frequency (f)
0-4	10
5-9	12
10-14	6
15-19	2
>19	0

• We know that 10 children have bought either 0, 1, 2, 3 or 4 CDs, but we do not know exactly how many each child bought.
• If we assumed that each child bought 4 CDs, it is likely that our estimate of the mean would be too big.
• If we assumed that each child bought 0 CDs, it is likely that our estimate would be too small.
• It therefore seems sensible to use the mid-point of the group and assume that each child bought 2.

Finding the mid-points of the other groups, we get:

 

Number of CDs	f	Mid-point, x	fx
0-4	10	2	20
5-9	12	7	84
10-14	6	12	72
15-19	2	17	34
>19	0	-	0

The mean is 

Remember: This is only an estimate of the mean.

The median

As explained previously, the median is the middle value when the values are arranged in order of size.

As the data has been grouped, we cannot find an exact value for the median, but we can find the class which contains the median.

 

Number of CDs	Frequency (f)
0-4	10
5-9	12
10-14	6
15-19	2
>19	0

There are 30 children, so we are looking for the class which contains the (30 + 1) ÷ 2 = 15¹₂th value. The median is therefore within the 5-9 class.

The mode

The mode is the most common value.

We cannot find an exact value for the mode, and therefore give themodal class. The modal class is 5-9.