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.

71.36 and 8.45

Variance = 78.5

Standard Deviation = 8.86

Step-by-step 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)