Calculate the standard deviation for the following data.

3, 4, 5, 6, 7

Correct option is C

Given:

Data: 3, 4, 5, 6, 7

Concept Used:

Mean: The average of the data points.

Variance: The average of the squared differences from the mean.

Standard Deviation: The square root of the variance.

Solution:

Mean =$$\frac{(3 + 4 + 5 + 6 + 7) }{ 5}$$​​

Mean = $$\frac{25 }{ 5}$$​​

Mean = 5

Calculate the squared differences from the mean:

(3 - 5)² = (-2)² = 4

(4 - 5)² = (-1)² = 1

(5 - 5)² = 0² = 0

(6 - 5)² = 1² = 1

(7 - 5)² = 2² = 4

Calculate the variance:

Variance =$$\frac{(4 + 1 + 0 + 1 + 4) }{ 5}$$​​

Variance = $$\frac{10 } {5}$$​​

Variance = 2

Calculate the standard deviation:

Standard Deviation = $$\sqrt{\text{Variance}}$$​​

Standard Deviation = $$\sqrt2$$​​