Question

11

Adimas found the mean of her 11 math test scores for the first semester.
(76 +87 +65 +88 +67+84 +77 +82 +91 +85 +90) 892
81
11
Using 81 as the mean, find the variance of her grades rounded to the nearest hundredth.
02=
Find the standard deviation of her grades rounded to the nearest hundredth.

Answer 1

71.36 and 8.45

Explanation:

Answer 2

Variance = 78.5

Standard Deviation = 8.86

Explanation:

Given

Mean = 81

Required

Find the variance and standard deviation of the given set of data.

Provided that we already know the mean; to calculate the variance, follow the steps below.

1. Subtract the mean from each data.

76 - 81 = -5

87 - 81 = 6

65 - 81 = -16

88 - 81 = 7

67 - 81 = -14

84 - 81 = 3

77 - 81 = -4

82 - 81 = 1

91 - 81 = 10

85 - 81 = 4

90 - 81 = 9

2. Square these results

-5² = 25

6² = 36

-16² = 256

7² = 49

-14² = 196

3² = 9

-4² = 16

1² = 1

10² = 100

4² = 16

9² = 81

3. Sum these results

Sum = 25+36+256+49+196+9+16+1+100+16+81

Sum = 785

4. Calculate variance by dividing the sum by n - 1 where n = 11

So, n - 1 = 11 - 1 = 10

Variance = 785/10

Variance = 78.50

5. Calculate standard deviation by finding the square root of variance

S.D = √78.50

S.D = 8.86 (Approximated)