# 8.4.4 Measures of Dispersion for Ungrouped Data, SPM Paper (Long Questions)

Question 7:
A set of data consists of twelve positive numbers.

Find
(a) the variance
(b) the mean

Solution:
(a)

(b)

Question 8:
A set of examination marks x1, x2, x3, x4, x5, x6 has a mean of 6 and a standard deviation of 2.4.
(a) Find
(i) the sum of the marks, $\Sigma x$ ,
(ii) the sum of the squares of the marks, $\Sigma {x}^{2}$ .

(b)
Each mark is multiplied by 2 and then 3 is added to it.
Find, for the new set of marks,
(i) the mean,
(ii) the variance.

Solution:
(a)(i)

(a)(ii)

(b)(i)
Mean of the new set of numbers
= 6(2) + 3
= 15

(b)(ii)
Variance of the original set of numbers
= 2.42 = 5.76

Variance of the new set of numbers
= 22 (5.76)
= 23.04