Download Working with grouped data It is sometimes easiest to work with data

Working with grouped data
It is sometimes easiest to work with data where you have frequencies of values
instead of a long list of single values. For example, instead of using a list such as
this
3,5,6,4,3,5,4,4,7,8,3,5,6,4,5,5,6
your data is in a table like this
VALUE
3
4
5
6
7
8
FREQUENCY
3
4
5
3
1
1
Product
9
16
25
18
7
8
For the list, you need to add all together, 3+5+6+…+5+6 = 83
For the table, you add the products, 3*3 + 4*4 + … + 8*1 = 83
MEAN
The mean of grouped data, then, is the sum of the products divided by N.
To do this in Excel or a similar spreadsheet, let us say that the values are in
column A (rows 1 to 6) and the frequencies column B. We will put the mean (the
average) in cell C1.
=SUMPRODUCT(A1:A6,B1:B6)/SUM(B1:B6)
For our example, this = 4.9
VARIANCE of a sample
There is a formula for calculating the variance of grouped data, as shown below
in Figure 1. In excel, we will use the first version of the equation. This sums the
products of (the frequency of each value) x ((the difference of each value from
the mean)squared), divided by N-1 (since we are interested in the variance of a
sample, not the variance of a population):
=SUMPRODUCT(B1:B6,(A1:A6-C1)^2)/(SUM(B1:B6)-1)
Let us put the variance (1.99) in C2.
Standard Deviation for a sample
The S.D. is just the square root of the variance, which is excel is
=SQRT(C2)
=1.41
Fig. 1. Calculating the variance for grouped data
(source:
http://www.lboro.ac.uk/media/wwwlboroacuk/content/mlsc/downloads/var_
stand_deviat_group.pdf ).