Question

find the sample variance, standard deviation, and range of the data. 7, 5, 9, 7, 2,...

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

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

Homework Answers

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

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