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Question: The quiz scores of 50 students of a class is as shown in the frequency distribution.
Quiz scoreFrequency
0 - 26
3 - 513
6 - 89
9 - 1114
12 - 148

Find the variance and standard deviation.


A ) 7.3 and 68.14
B ) 3.89 and 1.97
C ) 3.89 and 15.15
D ) 15.15 and 3.89

Steps to derive

1 The midpoint of each class (quiz score) and the product with the frequency is as shown in the table.


2 Variance of the sample,
s2 = Σ fX2-[(Σ f X)2n]n-1
 [Use n = ∑ f.]

3 = 3407-[(365)250]49

4 = 3407-2664.549

5 = 742.549 = 15.15

6 So, the sample variance is 15.15.

7 Sample standard deviation, s = sample variance =15.15 = 3.89

8 So, the sample standard deviation is 3.89.

9 The quiz scores of 50 students of a class has a sample variance of 15.15 and a sample standard deviation of 3.89.



Hence the right answer is Option D

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