Question

Find the standard deviation of the data summarized in the given frequency distribution.

The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Find the standard deviation. Round your answer to one decimal place.

Group of answer choices

7.0 min

4.5 min

4.8 min

5.0 min

Answer 1

Midpoint of classes = (Lower limit + upper limit ) / 2

So,

Midpoint for class 0 - 3 = 0 + 3 / 2 = 1.5

Similarly, midpoint for class 4-7 = 5.5

midpoint for class 8-11 = 9.5

midpoint for class 12-15 = 13.5

midpoint for class 16-19 = 17.5

midpoint for class 20-23 = 21.5

Let midpoint be X and number of customers be f

Mean = $\sum$ X * f / $\sum$f

= (1.5 * 9 + 5.5 * 16 + 9.5 * 15 + 13.5 * 8 + 17.5 * 0 + 21.5* 2) / 50

= 7.9

Standard deviation = sqrt [ $\sum$ X² * f - n * mean² / n-1 ]

= sqrt [ (1.5² * 9 + 5.5² * 16 + 9.5² * 15 + 13.5² * 8 + 17.5² * 0 + 21.5² * 2) - 50 *7.9² / 49 ]

= 4.8