Question

1. Consider the following sample dataset: 68359

i. Obtain the mean and variance

ii. If the sample number is subtracted from each of the value of the dataset, which of the above two parameters will remain unchanged? Explain briefly. (Note that no marks are awarded without an explanation.)

Answer 1

(i)sample data set is 6 8 3 5 9

Mean = (sum of all data values)/(total number of data values)

= (6+8+3+5+9)/5

= 6.2

and

variance =

using the data values

(ii) sample number is sample size, which is equal to 5. If we subtract 5 from each value, then new data set will be

1,3,-2,0,4

In this case, mean will be changed because the sum of all values is reduced, but the number of data values remain same, i.e. 5.

So, mean will be reduced.

Variance will remain unchanged because the variance is the measure of spread of data and spread of data or difference between the data values is still same irrespective of subtracting 5 from each value.

Therefore, mean will change and variance will remain unchanged.