STANDARD DEVIATION WORKSHEET

1. Find the standard deviation and the coefficient of variation for the following numbers: 5, 8, 9, 2, 6.

2. Find the standard deviation for the following distribution :

3. Find the standard deviation of first n natural numbers.

4. Find the standard deviation of first 25 natural numbers.

5. If arithmetic mean and coefficient of variation of x are 10 and 40 respectively, what is the variance of (15 – 2x) ?

1. Answer :

Formula for standard deviation for an ungrouped data :

The coefficient of variation is

2. Answer :

Formula for standard deviation for a grouped frequency distribution :

3. Answer :

Let x_i = 1, 2, 3, ..........n.

Arithmetic mean of first n natural numbers :

Standard deviation of first n natural numbers :

4. Answer :

Standard deviation of first n natural numbers :

Substitute n = 25.

5. Answer :

Let y = 15 - 2x.

When x and y are related as y = a + bx, then

S_y = |b|S_x

S_y = |-2|S_x

S_y = 2S_x ----(1)

Coefficient of variation of x = 40 and mean of x = 10.

Coefficient of variation of x = 40

100 ⋅ (S_x/AM) = 40

100 ⋅ (S_x/10) = 40

10 ⋅ S_x = 40

S_x = 4

S_y = 2 ⋅ 4

S_y = 8

Variance of y = 8²

Variance of (15 - 2x) = 64

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