Question

a. A data set has n items. The sum of the items is 800 and the mean is 20. Find n

b. The standard deviation of this data set is 3. Each value in the set is multiplied by 10. Write down the value of the new mean.

c. Find the value of the new variance.

Answer 1

a.

Data Set has n items : x_i i = 1,2,3,..n

Sum of the items = = 800

Mean = = 20

n = 40

b.

if Y=aX

then Mean Y = a Mean of X

Variance of Y = a² Variance of X

Y : new data set

X: Old data set

Each value in the set is multiplied by 10 i.e

Y = 10 X

Mean of X = 20

Mean of Y = 10 * Mean of X = 10 * 20 = 200

Value of the new mean = 200

c.

Standard deviation of the data set X = 3

Variance of X = 3 * 3 =9

Variance of Y = 10² * Variance of X = 100 * 9 = 900

value of the new variance = 900