The following is the frequency distribution for the speed of a sample of automobiles traveling on an interstate highway. The standard deviation is
A) 9.06.
B) 9.28.
C) 86.19.
D) 82.09.

Question

The following is the frequency distribution for the speed of a sample of automobiles traveling on an interstate highway.  The standard deviation is
A) 9.06. 
B) 9.28. 
C) 86.19. 
D) 82.09.

Quizplus · Accepted Answer

To find the standard deviation, we need to find the mean first. We can find the mean by using the formula: 
mean = sum of (frequency × midpoint) / sum of frequency

Here, sum of frequency = 50

midpoint = (lower class limit + upper class limit) / 2

For example, the midpoint for the first class interval (30 - 39.9) is:
midpoint = (30 + 39.9) / 2 = 34.95

Using these formulas, we can find the mean to be approximately 55.56.

Next, we need to find the sum of squared deviations from the mean. For each class interval, we can calculate the deviation from the mean by subtracting the mean from the midpoint, and then squaring the result. For example, the deviation from the mean for the first class interval (30 - 39.9) is:

deviation = 34.95 - 55.56 = -20.61
squared deviation = (-20.61)² = 424.97

We can repeat this process for each class interval and sum the results. Doing this, we get a sum of squared deviations from the mean of approximately 26567.86.

Finally, we can calculate the standard deviation using the formula:

standard deviation = square root of (sum of squared deviations / number of observations)

Here, the number of observations is the sum of the frequencies, which is 50. Substituting the values we have found, we get:

standard deviation = square root of (26567.86 / 50) = 9.28

Therefore, the answer is B.

The Following Is the Frequency Distribution for the Speed of a Sample