Question

A die is rolled 30 times and the
following distribution is obtained
Score -1 2 3 4 5 6
frequency- 2 6 2 5 10 5
Find Range ,variance and Standard Deviation.​

Answer 1

Following is the Range, Variance and Standard Deviation of the given distribution:

                               X                    X²

                               2                     4

                               6                    36

                               2                     4

                               5                    25

                               10                  100

                               5                     25      

Here, n=6

Range : 8

• The range is the difference between the smallest data value and the largest data value.

• As per question, the smallest data value is 2 and the largest data value is 10.

• Thus, Range = 10−2

                              = 8

Variance : 8.8

• Now, ∑x = 30

                ∑x² = 194

               (∑x)²= 900

• ∴  s² = (∑x² - (∑x)²/n) / (n - 1)

                 = (∑x² - (∑x)²/6) / (6 - 1)

                 = 44/5

                 = 8.8

Standard Deviation : 2.9665

• It can be calculated as the under root of variance, i.e

= $\sqrt{variance}$

= 2.9665