suppose a bank branch, located in a residential area, is connected with its serv

Question

suppose a bank branch, located in a residential area, is connected with its service during the noon-to-1 pm lunch hour. The waiting times, in minutes, collected from a sample of 15 customers during this hour, are listed below. Complete parts (a) through (d) below. 9.64 5.98 7.98 5.85 8.76 3.83 8.01 8.38 10.39 6.73 5.68 4.11 6.15 9.93 5.57 a). Compute the mean and median. The mean is ________ The median is _________ b) Compute the variance, standard deviation, range, coefficient of variation, and Z scores. Are there any outliers? Explain. The variance is ________ The standard deviation is _________ The range is _________ The coefficient of variation is __________ Compute the Z scores. Data (x) Z Score 9.64 ? 5.98 ? 7.98 ? 5.85 ? 8.76 ? 3.83 ? 8.01 ? 8.38 ? 10.39 ? 6.73 ? 5.68 ? 4.11 ? 6.15 ? 9.93 ? 5.57 ? Are there any outliers? Explain. A. Yes, since there are no Z scores that are less than - 3.0 or greater than +3.0. B. No, since there are no Z scores that are less than - 3.0 or greater than +3.0 C. No, since there is at least one Z score that is less than - 3.0 or greater than +3.0 D. Yes, since there is at least one Z score that is less than -3.0 or greater than +3.0 c). Are the data skewed? If so, how? Choose the correct response below. A. Yes, the data are right-skewed because the mean is greater than the median. B. Yes, the data are left-skewed because the mean is less than the median. C. No, the data are not skewed because the mean and median are equal. d). As a customer walks into the branch office during the lunch hour, he asks the branch manager how long he can expect to wait. The branch manager replies, " Almost certainly less than 5 minutes." On the basis of the results of (a) through (c), evaluate the accuracy of this statement. Choose the correct response below. A. Although both the mean and median are greater than 5 minutes, all values greater than 5 minute have a Z score greater than +3.0, thus they are outliers. This means the branch manager's statement is accurate. B. Since the mean and median are both greater than 5 minutes, the customer is likely to experience a waiting time in excess of 5 minutes. C. Since the range of value is greater than 5 minutes, the customer is likely to experience a waiting time in excess of 5 minutes.

Explanation / Answer

ANSWER:

Mean, Median, Mode, and Range

Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all.

The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first. The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.

The "range" is just the difference between the largest and smallest values.

Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is the usual average, so:

(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

Note that the mean isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.

The median is the middle value, so I'll have to rewrite the list in order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

13, 13, 13, 13, 14, 14, 16, 18, 21

So the median is 14. Copyright © Elizabeth Stapel 2004-2011 All Rights Reserved
The mode is the number that is repeated more often than any other, so 13 is the mode.

The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.

mean: 15
median: 14
mode: 13
range: 8

Note: The formula for the place to find the median is "( [the number of data points] + 1) ÷ 2", but you don't have to use this formula. You can just count in from both ends of the list until you meet in the middle, if you prefer. Either way will work.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.