Statistics Short Questions (Question 1 & 2)


Question 1:
Given that the standard deviation of five numbers is 6 and the sum of the squares of these five numbers is 260.  Find the mean of this set of numbers.

Solution:
Given that σ=6Σ x 2 =260. σ=6 Σ x 2 n X ¯ 2 =6 Σ x 2 n X ¯ 2 =36 260 5 X ¯ 2 =36 X ¯ 2 =16 X ¯ =±4 mean = ±4



Question 2:
Both of the mean and the standard deviation of 1, 3, 7, 15, m and n are 6.  Find
(a) the value of m + n,
(b) the possible values of  n.

Solution:
(a)
Given mean = 6 Σx n =6 Σx 6 =6 
1 + 3 + 7 + 15 + m + n = 36
26 + m + n = 36
m + n = 10

(b)
σ=6 σ 2 =36 Σ x 2 n X ¯ 2 =36 1+9+49+225+ m 2 + n 2 6 6 2 =36 284+ m 2 + n 2 6 36=36 284+ m 2 + n 2 6 =72 284+ m 2 + n 2 =432 m 2 + n 2 =148 From (a), m=10n ( 10n ) 2 + n 2 =148 10020n+ n 2 + n 2 =148 2 n 2 20n48=0 n 2 10n24=0 ( n6 )( n+4 )=0 n=6 or 4