Question

Compute the standard deviation of the following set of data to the nearest whole number: 10, 15, 15, 20, 20

Answer 1

Answer:

For the given set of numbers, the standard deviation is 4 (Rounding to the nearest whole number).

Step-by-step explanation:

1. The first step for finding the standard deviation is to find the mean of the set of numbers.

Mean = ( 10 + 15 + 15 + 20 +20)/5

Mean = 80/5 = 16

Mean = 16

2. The second step is to find the variance.

Let's recall that the variance is the sum of all the squared differences of each element of the set minus the mean over the number of terms less one, if we want to be strict.

Variance = [6² + 1² + 1² + (-4)² + (-4)²]/4

Variance = [36 + 1 + 1 + 16  + 16]/4

Variance = 70/4

Variance = 17.5

3. Now we'r ready to calculate the standard deviation.

Standard deviation = √ Variance

Standard deviation = √ 17.5

Standard deviation = 4.18

Standard deviation = 4 (Rounding to the nearest whole number)