For the data set 7,5,10,11,12 the mean is x, is 9. What is the standard deviation?

SD (σ) = 2.91548

Step-by-step explanation:

Definition:

Standard deviation (SD) measures the volatility or variability across a set of data. It is the measure of the spread of numbers in a data set from its mean value and can be represented using the sigma symbol (σ)

To find out SD you must know the value of Mean and Variance.

Mean=sum of values / N (number of values in set)

Mean=7+5+10+11+12/5

Mean=45/5

Mean=9

Variance = ((n1 - Mean) 2 + ... nn - Mean) 2) / N-1 (number of values in set - 1)

Variance = ((7-9) ^2 + (5-9) ^2 + (10-9) ^2 + (11-9) ^2 + (12-9) ^2)) / 5-1

Variance = ((-2) ^2 + (-4) ^2 + (1) ^2 + (2) ^2 + (3) ^2) / 4

Variance = (4+16+1+4+9) / 4

Variance=34/4

Variance=8.5

Standard Deviation (σ) = √Variance

σ = √8.5

By taking the square root of √8.5 we get;

σ = 2.91548

Thus the value of Standard Deviation (σ) = 2.91548 ...