Customers waiting at Ellerton Bank have been complaining about the amount of time they must wait in line. Managers at the bank, beginning to investigate the problem, have recorded sample waiting times for
8
customers at the bank. Here are the
8
waiting times (in minutes).
23
,
15
,
13
,
20
,
23
,
21
,
24
,
23
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(a) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place.
(b) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable.
zero modes
one mode:
two modes: and
(a) To find the median of the data set, we first need to arrange the waiting times in ascending order:
13, 15, 20, 21, 23, 23, 23, 24.
The median is the middle value in the data set. Since there are 8 data points, the median will be the average of the 4th and 5th values: (21 + 23) / 2 = 22.
Therefore, the median of this data set is 22.
(b) To find the mean of the data set, we add up all the waiting times and divide by the number of data points:
(13 + 15 + 20 + 21 + 23 + 23 + 23 + 24) / 8 = 162 / 8 = 20.25.
Therefore, the mean of this data set is 20.25.
(c) To determine the mode(s) of the data set, we look for the value(s) that appear most frequently. In this case, there is no value that appears more than once.
Therefore, the data set has zero modes.
Adults who are being tested for dementia are asked to perform mental tasks such as listing as many animals as they can in one minute. Here are the numbers of animals listed in one minute by
10
adults.
25
,
18
,
16
,
12
,
17
,
23
,
20
,
13
,
13
,
19
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(a) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place.
(b) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable.
zero modes
one mode:
two modes: and
(a) To find the mean of the data set, we add up all the numbers of animals listed and divide by the number of adults:
(25 + 18 + 16 + 12 + 17 + 23 + 20 + 13 + 13 + 19) / 10 = 176 / 10 = 17.6.
Therefore, the mean of this data set is 17.6.
(b) To find the median of the data set, we first need to arrange the numbers in ascending order:
12, 13, 13, 16, 17, 18, 19, 20, 23, 25.
The median is the middle value in the data set. Since there are 10 data points, the median will be the average of the 5th and 6th values: (17 + 18) / 2 = 17.5.
Therefore, the median of this data set is 17.5.
(c) To determine the mode(s) of the data set, we look for the value(s) that appear most frequently. In this case, the value 13 appears twice, which is more than any other value.
Therefore, the data set has one mode, which is 13.
Adults who are being tested for dementia are asked to perform mental tasks such as listing as many animals as they can in one minute. Here are the numbers of animals listed in one minute by
9
adults.
22
,
21
,
11
,
24
,
23
,
10
,
17
,
20
,
25
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(a) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place.
(b) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable.
zero modes
one mode:
two modes: and
(a) To find the median of the data set, we first need to arrange the numbers in ascending order:
10, 11, 17, 20, 21, 22, 23, 24, 25.
The median is the middle value in the data set. Since there are 9 data points, the median will be the value in the 5th position, which is 21.
Therefore, the median of this data set is 21.
(b) To find the mean of the data set, we add up all the numbers of animals listed and divide by the number of adults:
(22 + 21 + 11 + 24 + 23 + 10 + 17 + 20 + 25) / 9 = 173 / 9 = 19.2.
Therefore, the mean of this data set is 19.2.
(c) To determine the mode(s) of the data set, we look for the value(s) that appear most frequently. In this case, there are no values that appear more than once.
Therefore, the data set has zero modes.
Here are the numbers of calls received at a customer support service during
8
randomly chosen, hour-long intervals.
8
,
10
,
24
,
15
,
11
,
6
,
20
,
6
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(a) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place.
(b) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable.
zero modes
one mode:
two modes: and
(a) To find the mean of the data set, we add up all the numbers of calls received and divide by the number of intervals:
(8 + 10 + 24 + 15 + 11 + 6 + 20 + 6) / 8 = 100 / 8 = 12.5.
Therefore, the mean of this data set is 12.5.
(b) To find the median of the data set, we first need to arrange the numbers in ascending order:
6, 6, 8, 10, 11, 15, 20, 24.
The median is the middle value in the data set. Since there are 8 data points, the median will be the average of the 4th and 5th values: (10 + 11) / 2 = 10.5.
Therefore, the median of this data set is 10.5.
(c) To determine the mode(s) of the data set, we look for the value(s) that appear most frequently. In this case, the values 6 and 24 both appear twice, which is more than any other value.
Therefore, the data set has two modes, which are 6 and 24.
The following list contains the average annual total returns (in percentage points) for
9
mutual funds. The mutual funds appear in an online brokerage firm's "all-star" list.
8
,
33
,
21
,
30
,
8
,
30
,
35
,
30
,
8
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(a) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place.
(b) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable.
zero modes
one mode:
two modes: and
(a) To find the median of the data set, we first need to arrange the average annual total returns in ascending order:
8, 8, 8, 21, 30, 30, 30, 33, 35.
The median is the middle value in the data set. Since there are 9 data points, the median will be the value in the 5th position, which is 30.
Therefore, the median of this data set is 30.
(b) To find the mean of the data set, we add up all the average annual total returns and divide by the number of mutual funds:
(8 + 33 + 21 + 30 + 8 + 30 + 35 + 30 + 8) / 9 = 203 / 9 = 22.6.
Therefore, the mean of this data set is 22.6.
(c) To determine the mode(s) of the data set, we look for the value(s) that appear most frequently. In this case, the value 8 appears three times, which is more than any other value.
Therefore, the data set has one mode, which is 8.
To find the median, mean, and mode(s) of the given data set, you can follow these steps:
(a) Median:
The median is the middle value in a dataset when it is ordered in ascending or descending order. To find the median, first, arrange the waiting times in ascending order: 13, 15, 20, 21, 23, 23, 23, 24.
Since there are 8 values in the dataset, the middle two values are 20 and 21. To find the median, take the average of these two values: (20 + 21) / 2 = 20.5. Rounding to one decimal place, the median is 20.5.
(b) Mean:
The mean is calculated by adding up all the values in the dataset and then dividing the sum by the total number of values. Summing up the waiting times: 23 + 15 + 13 + 20 + 23 + 21 + 24 + 23 = 162.
Divide the sum by the number of values (8) to find the mean: 162 / 8 = 20.25. Rounding to one decimal place, the mean is 20.3.
(c) Mode(s):
A mode is the value(s) that appear most frequently in a dataset. Count the frequency of each waiting time: 13 (1), 15 (1), 20 (1), 21 (1), 23 (3), 24 (1).
In this dataset, the mode(s) is the value(s) that have the highest frequency. Here, the value 23 appears 3 times, which is the highest frequency. So, the dataset has one mode: 23.
In conclusion:
(a) The median of the data set is 20.5
(b) The mean of the data set is 20.3
(c) The data set has one mode: 23.