Question

In a statistic class, 10 scores were randomly selected with the following results were obtained (mean=71.5): 74, 73, 77, 77, 71, 68, 65, 77, 67, 66 What is the variance? please show each way there is to work this problem- and explain! show all work possible thanks

Answer 1

solution

given data

74, 73, 77, 77, 71, 68, 65, 77, 67, 66

mean = 71.5

Sample standard deviation is s

s = 1/(n-1)(x - )²

⁼  1/10 - 1  (74 - 71.5 )²+ (73 - 71.5 )²+ (77 - 71.5)²+ (77- 71.5 )² +(71- 71.5 )² +(68- 71.5 )²+ (65 - 71.5 )²+ (77 - 71.5)²+ (67- 71.5 )² +(66- 71.5 )²

= 1/9 (6.25+2.25+30.25+30.25+0.25+12.25+42.25+30.25+20.25+30.25)

= 204.5/9

= 22.72222222

= 4.766788 (rounded)

The sample standard deviation is 4.7668

variance =  (s )²

⁼ (4.7668 )²

   ^{= 22.72238 ( rounded)}

^{variance = 22.72}