Question

The reading rate for 60 students is shown in the frequency table below.

Answer 1

The standard deviation is 15.76. The typical reading rate for the data set varies from the mean by an average of 15.76 words per minute.

How to determine the standard deviation of the data set?

The dataset is given as:

Reading Rate

(words per minute) Frequency

60 6

65 8

70 12

75 5

80 1

85 1

90 2

95 5

100 20

Calculate the mean using

Mean = Sum/Count

So, we have

Mean = (60 * 6 + 65 * 8 + 70 * 12 + 75 * 5 +  80 * 1 +  85 * 1 +  90 * 2 +  95 * 5 + 100 * 20)/(6 + 8 + 12 + 5 + 1 + 1 + 2 + 5 + 20)

Evaluate

Mean = 81.92

The standard deviation is

$\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f -1}}$

So, we have:

SD = √[6 * (60 - 81.92)^2 + 8 * (65 - 81.92)^2 + 12 * (70 - 81.92)^2 + 5 * (75 - 81.92)^2 + 1 * (80 - 81.92)^2 +  1 * (85 - 81.92)^2 +  2 * (90  - 81.92)^2 + 5 * (95 - 81.92)^2 + 20 * (100 - 81.92)^2)]/[(6 + 8 + 12 + 5 + 1 + 1 + 2 + 5 + 20 - 1)]

This gives

SD = √248.382779661

Evaluate

SD = 15.76

Hence. the standard deviation is 15.76. The typical reading rate for the data set varies from the mean by an average of 15.76 words per minute.

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