Question

What is the standard deviation of the data set given below 5 7 9 11 13

Answer 1

Answer:

3.1623 (sqrt(10))

Step-by-step explanation:

Standard Deviation is calculated by first squaring the differences between the observations and the mean and then taking the square root of the sum of the squares of the differences divided by the number of observations - 1.

Mean = Sum of Observations/Total Observations

Mean = (5 + 7 + 9 + 11 + 13)/5 = 45/5 = 9.

Square of the mean = 9^2 = 81.

Now subtracting the mean from each observation and squaring it gives:

(5 - 9)^2 = (-4)^2 = 16

(7 - 9)^2 = (-2)^2 = 4

(9 - 9)^2 = (0)^2 = 0

(11 - 9)^2 = (2)^2 = 4

(13 - 9)^2 = (4)^2 = 16

Sum of squares = 16 + 4 + 0 + 4 + 16 = 40.

Standard deviation = sqrt(40/4) = sqrt(10) = 3.16 (correct to 2 decimal places).

Therefore, answer is 3.16!!!