Question

find the sample variance, standard deviation, and range of the data.

7, 5, 9, 7, 2, 4, 3, 2, 3, 8

Answer 1

Solution:

Given that,

2,2,3,3,4,5,7,7,8,9

n = 10

The mean of sample is   

x/n =  (2 +2 + 3 +3 + 4 + 5 + 7 +7 +8 + 9 / 10)

   = 50 / 10

= 5

The sample mean is 5

Sample variance is s²

s² = 1/(n-1)(x - )²

⁼  1/(10 - 1) (2 - 5 )²+ (2 - 5 )²+ (3 - 5 )²+ (3 - 5 )² +( 4 - 5 )² + (5 - 5 )²+ (7 - 5 )²+ (7 - 5 )²+ (8 - 5 )² +( 9 - 5 )²

= 1/9 (9 + 9 + 4+ 4 + 1 + 0 + 4 + 4 + 9 + 16)

= 60 /9

= 6.67

The sample variance is = 6.67

b) Sample standard deviation is = s = s²

Sample standard deviation is = s = 6.67

Sample standard deviation is = s = 2.58

c) The range = 9 - 2 = 7