Estimating the standard deviation or variance 0.9 *** 2.4 2.5 *** 3.1 *** 4.0 4.

Question

Estimating the standard deviation or variance

0.9

***

2.4

2.5

***

3.1

***

4.0

4.3

4.3

4.4

4.4

***

4.9

4.9

5.1

5.2

***

5.6

5.8

Consider the sample of n =20 scores. Notice that they are listed in order from 0.9 to 5.8, but that some of the scores are obscured by ***, The mean , M, of these scores is 4.0.

Suppose you are asked for the sample standard deviation of these scores. Since you don’t have all of them, you cannot calculate it. Which of the following is the estimate of the sample standard deviation?

A. 0.3

B. 4.9

C. 3.7

D, 1.4

0.9

***

2.4

2.5

***

3.1

***

4.0

4.3

4.3

4.4

4.4

***

4.9

4.9

5.1

5.2

***

5.6

5.8

Explanation / Answer

5 out of 20 values are missing.

Sum of these 15 values = 61.8

Mean of these 15 values = 4.12

Sum of missing 5 values = 20*4 - 61.8 = 18.2

Mean of missing 5 values = 3.64

So, we approximate the missing 5 values as 3.64

Since all the other given values are only upto 1 decimal place, we cannot approximate the missing 5 values equal to 3.64, since it has 2 decimal points precision:

We choose the following set of values, trying to minimize the deviation as much as possible:

3.6, 3.6, 3.6, 3.7, 3.7

Using the new set of values, we calculate the sample standard deviation as:

1.18

Thus we can approximate the sample standard deviation as 1.4

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