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QUESTION 1 1 points Save An swer 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 Waiting time Number of (minutescustomer 0-3 4-7 8 11 12 15 16-19 20-23 12 10 12 0 5.4 5.6 7.0

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Answer #1

Standard deviation for frequency distribution:

The formula for standard deviation

n _ rl

Where x - mid point of the class interval

f - frequency of each class interval

mear

The formula to find the mid point is,

Lower limit + Upper limit

For first class 0 - 3, the midpoint is

0+3 = 1.5

Similarly the midpoints of the classes are 5.5, 9.5, 13.5, 17.5 and 21.5 respectively.

Number of customers are nothing but the frequencies.

f- 50 rt

The formula of mean is

Lfx 1.5 *14 +5.5 12 +9.5 10 13.51217.50+21.5*2 50

fx 387 50 7.74

The standard deviation is,

2. (1.5-7.74)2 * 14 + 5.5-7.74)2 * 12 + (9.5-7.74)2 * 10 + (13.5-7.74)2 * 12 + (17.5-7.74)2 *0+ 21.5-7.74)2 * 2 50-1 (z ー

1413.1254 49

Standard deviation = 5.4

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