Find the standard deviation for 15,16,16,16,17,18,21?

To find the standard deviation, we first need to calculate the mean of the data set:

(15 + 16 + 16 + 16 + 17 + 18 + 21) / 7 = 119 / 7 = 17

Next, we calculate the squared differences between each data point and the mean:

(15-17)^2 = 4
(16-17)^2 = 1
(16-17)^2 = 1
(16-17)^2 = 1
(17-17)^2 = 0
(18-17)^2 = 1
(21-17)^2 = 16

Then, we calculate the variance by finding the average of these squared differences:

(4 + 1 + 1 + 1 + 0 + 1 + 16) / 7 = 24 / 7 = 3.43

Finally, we find the standard deviation by taking the square root of the variance:

√3.43 ≈ 1.85

Therefore, the standard deviation for the data set 15, 16, 16, 16, 17, 18, 21 is approximately 1.85.

1. Find the mean:

Mean = (15 + 16 + 16 + 16 + 17 + 18 + 21) / 7 = 17

2. Find the variance:

Variance = [(15 - 17)^2 + (16 - 17)^2 + (16 - 17)^2 + (16 - 17)^2 + (17 - 17)^2 + (18 - 17)^2 + (21 - 17)^2] / 6 = 4.17

3. Find the standard deviation:

Standard deviation = sqrt(4.17) = 2.04