Bids were placed in a silent auction for a sword reputed to have been used at the Battle of Hastings, worth a reported
$20,000
. The respective bids (in thousands of dollars) placed by the
10
bidders were as follows.
26
,
18
,
18
,
14
,
18
,
13
,
12
,
14
,
14
,
30
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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 values and divide by the number of values.
Mean = (26 + 18 + 18 + 14 + 18 + 13 + 12 + 14 + 14 + 30) / 10
Mean = 177 / 10
Mean = 17.7
The mean of this data set is 17.7.
(b) To find the median of the data set, we first need to arrange the values in ascending order.
12, 13, 14, 14, 14, 18, 18, 18, 26, 30
Since there are 10 values, the median will be the average of the 5th and 6th values.
Median = (14 + 18) / 2
Median = 32 / 2
Median = 16
The median of this data set is 16.
(c) To determine the modes of the data set, we look for the values that appear the most frequently. In this case, the value 14 appears 3 times, which is more than any other value.
Therefore, the data set has one mode, which is 14.
To begin to better understand personal experiences of headache pain, a drug manufacturer has asked
9
adults to rate their most recent headache on a scale of
0
to
100
(with
0
corresponding to no pain and
100
corresponding to the greatest pain the person has ever felt). Here are the
9
ratings.
32
,
10
,
63
,
24
,
12
,
65
,
65
,
14
,
65
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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.
12
(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 values in ascending order.
10, 12, 14, 24, 32, 63, 65, 65, 65
Since there are 9 values, the median will be the middle value.
Median = 32
The median of this data set is 32.
(b) To find the mean of the data set, we add up all the values and divide by the number of values.
Mean = (32 + 10 + 63 + 24 + 12 + 65 + 65 + 14 + 65) / 9
Mean = 350 / 9
Mean = 38.9
The mean of this data set is 38.9.
(c) To determine the modes of the data set, we look for the values that appear the most frequently. In this case, the value 65 appears 3 times, which is more than any other value.
Therefore, the data set has one mode, which is 65.
The following list contains the average annual total returns (in percentage points) for
8
mutual funds. The mutual funds appear in an online brokerage firm's "all-star" list.
37
,
9
,
14
,
−10
,
14
,
16
,
21
,
2
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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 values and divide by the number of values.
Mean = (37 + 9 + 14 - 10 + 14 + 16 + 21 + 2) / 8
Mean = 103 / 8
Mean = 12.9
The mean of this data set is 12.9.
(b) To find the median of the data set, we first need to arrange the values in ascending order.
-10, 2, 9, 14, 14, 16, 21, 37
Since there are 8 values, the median will be the average of the 4th and 5th values.
Median = (14 + 14) / 2
Median = 28 / 2
Median = 14
The median of this data set is 14.
(c) To determine the modes of the data set, we look for the values that appear the most frequently. In this case, there are no values that appear more than once, so there are zero modes.
Therefore, the data set has zero modes.
The following are the annual incomes (in thousands of dollars) for
10
randomly chosen, U.S. adults employed full-time.
76
,
81
,
35
,
76
,
91
,
76
,
74
,
52
,
36
,
78
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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 values in ascending order.
35, 36, 52, 74, 76, 76, 76, 78, 81, 91
Since there are 10 values, the median will be the average of the 5th and 6th values.
Median = (76 + 76) / 2
Median = 152 / 2
Median = 76
The median of this data set is 76.
(b) To find the mean of the data set, we add up all the values and divide by the number of values.
Mean = (76 + 81 + 35 + 76 + 91 + 76 + 74 + 52 + 36 + 78) / 10
Mean = 695 / 10
Mean = 69.5
The mean of this data set is 69.5.
(c) To determine the modes of the data set, we look for the values that appear the most frequently. In this case, the value 76 appears 3 times, which is more than any other value.
Therefore, the data set has one mode, which is 76.
A tour company in a major city has a daily sightseeing trip. Each day, tour officials record the number of people making the trip. The data for a selection of
8
summer days are as follows.
42
,
54
,
44
,
49
,
33
,
52
,
45
,
52
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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 values and divide by the number of values.
Mean = (42 + 54 + 44 + 49 + 33 + 52 + 45 + 52) / 8
Mean = 371 / 8
Mean = 46.4
The mean of this data set is 46.4.
(b) To find the median of the data set, we first need to arrange the values in ascending order.
33, 42, 44, 45, 49, 52, 52, 54
Since there are 8 values, the median will be the average of the 4th and 5th values.
Median = (45 + 49) / 2
Median = 94 / 2
Median = 47
The median of this data set is 47.
(c) To determine the modes of the data set, we look for the values that appear the most frequently. In this case, there are no values that appear more than once, so there are zero modes.
Therefore, the data set has zero modes.
To find the mean, median, and modes of this data set, follow these steps:
(a) To find the mean, add up all the values in the data set and then divide by the total number of values.
- Add up the values: 26 + 18 + 18 + 14 + 18 + 13 + 12 + 14 + 14 + 30 = 177
- Divide by the total number of values (10): 177 / 10 = 17.7
So the mean of this data set is 17.7 (rounded to one decimal place).
(b) To find the median, arrange the values in ascending order and find the middle value.
- Arrange the values in ascending order: 12, 13, 14, 14, 14, 18, 18, 18, 26, 30
- Since there are 10 values, the middle value would be the average of the fifth and sixth values: (14 + 18) / 2 = 16
So the median of this data set is 16.
(c) To find the modes, identify the value(s) that appear most frequently in the data set.
- The value 14 appears three times, while all other values appear only once or twice.
- Since 14 appears more frequently than any other value, it is the mode of this data set.
So the data set has one mode, which is 14.