(2)A die is rolled 30 times and the following distribution is obtained. Find the
variance and the standard deviation.
Score 1 2 3 4 5 6
Frequency 2 6 2 5 9 6
Repeat the experiment and construct the frequency table as shown above. Find its
mean and standard deviation.
Answers
Given : A die is rolled 30 times and the distribution is obtained.
To find : Mean , Variance & Standard deviation
Solution:
Score frequency score * frequency
1 2 2
2 6 12
3 2 6
4 5 20
5 9 45
6 6 36
Total 30 121
Mean = 121/30 = 4.03 ≈ 4
Score frequency (score - Mean)² * f
1 2 18
2 6 24
3 2 2
4 5 0
5 9 9
6 6 24
Total 30 75
Standard Deviation = √( 75/30 ) = √2.5
= 1.58
Variance = 2.5
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