For the data set 7,5,10,11,12 the mean is x, is 9. What is the standard deviation?
Accepted Solution
A:
Answer:SD(σ)=2.91548Step-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+12/5Mean=45/5Mean=9Variance=((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))/5-1Variance=((-2)^2+(-4)^2+(1)^2+(2)^2+(3)^2)/4Variance=(4+16+1+4+9)/4Variance=34/4Variance=8.5Standard Deviation(σ)=√Varianceσ = √8.5By taking the square root of √8.5 we get;σ = 2.91548Thus the value of Standard Deviation(σ)=2.91548....