Question

If the range of discrete data of n observations is zero, then:

• A. all values of data are zero
• B. all values of data are equal to standard deviation
• C. all values of data are equal
• D. the extreme values of data are different

Answer 1

The correct option is C all values of data are equal

Let m be the least value of the discrete data and M be the maximum value of the discrete data.
Then range = M – m = 0 (hypothesis)
$\therefore$ M = m
$\therefore$ m $⩽$ each data item $⩽$ M = m
$\Rightarrow$ each data item = m or M i.e, all values of the data are equal.