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 = 6 Σ 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 Σ x n = 6 Σ x 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 = 10 n ( 10 n ) 2 + n 2 = 148 100 20 n + n 2 + n 2 = 148 2 n 2 20 n 48 = 0 n 2 10 n 24 = 0 ( n 6 ) ( n + 4 ) = 0 n = 6  or  4

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