Answer:
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....
