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Question: The blood urea nitrogen (in milligrams per deciliter - mg/dl) count of 20 randomly selected patients is shown in the frequency distribution table.
Blood urea nitrogenFrequency
11 - 133
13 - 154
15 - 173
17 - 195
19 - 215

Find the variance and standard deviation.


A ) 6.7, 2.6
B ) 7.9, 2.8
C ) 8.4, 2.9
D ) 6.4, 2.5

Steps to derive

1 The midpoint of each class (blood urea nitrogen) 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 = 5604-[(330)220]19

4 = 5604-544519

5 = 15919 = 8.4

6 So, the sample variance is 8.4.

7 Sample standard deviation, s = sample variance = 8.4 = 2.9

8 So, the sample standard deviation is 2.9.

9 The blood urea nitrogen count of 20 patients has a sample variance of 8.4 and a sample standard deviation of 2.9.



Hence the right answer is Option C

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