Question

The data list shows the scores of ten students in Mr. Smith's math class. 61, 67, 81, 83, 87, 88, 89, 90, 98, 100 What is the standard deviation, to the nearest tenth, of the data if the scores represent a sample of Mr. Smith's students

Answer 1

12.3

Explanation:

Step 1

We find the mean

The data list shows the scores of ten students in Mr. Smith's math class. 61, 67, 81, 83, 87, 88, 89, 90, 98, 100

Mean = Sum of terms/Number of terms

Number of terms = 10

Mean = 61 + 67 + 81 + 83 + 87 + 88 + 89 + 90 + 98 + 100/10

Mean = 844/10

Mean = 84.4

Step 2

Standard deviation

The formula for sample standard deviation =

√(x - Mean)²/n - 1

= √[(61 - 84.4)² + (67 - 84.4)² + (81 - 84.4)² + (83 - 84.4)² + (87 - 84.4)² + (88 - 84.4)² + (89 - 84.4)² + (90 - 84.4)² + (98 - 84.4)² + (100 - 84.4)²]/10 - 1

=√ 547.56 + 302.76 + 11.56 + 1.96 + 6.76 + 12.96 + 21.16 + 31.36 + 184.96 + 243.36/10 - 1

= √1364.4/9

= √151.6

= 12.31259518

Approximately to the nearest tenth = 12.3

The standard deviation = 12.3