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.
2
,
−3
,
7
,
30
,
39
,
15
,
12
,
11
,
29
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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 a data set, we need to arrange the numbers in ascending order:
-3, 2, 7, 11, 12, 15, 29, 30, 39
Since there are 9 numbers in the data set, we need to find the middle number. In this case, the middle number is the 5th number, which is 12. Therefore, the median of this data set is 12.
(b) To find the mean of a data set, we need to sum up all the numbers and divide it by the total number of numbers.
Mean = (2 - 3 + 7 + 30 + 39 + 15 + 12 + 11 + 29) / 9 = 144 / 9 = 16.
Therefore, the mean of this data set is 16.
(c) A mode is the value that appears most frequently in a data set. In this case, there are no numbers that appear more than once, so there are zero modes.
Total blood cholesterol level was measured for each of
7
adults. Here are the
7
measurements (in mg/dL).
264
,
177
,
132
,
133
,
177
,
234
,
146
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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 a data set, we need to sum up all the numbers and divide it by the total number of numbers.
Mean = (264 + 177 + 132 + 133 + 177 + 234 + 146) / 7 = 1253 / 7 ≈ 179
Therefore, the mean of this data set is approximately 179.
(b) To find the median of a data set, we need to arrange the numbers in ascending order:
132, 133, 146, 177, 177, 234, 264
Since there are 7 numbers in the data set, the median is the middle number. In this case, the middle number is the 4th number, which is 177. Therefore, the median of this data set is 177.
(c) A mode is the value that appears most frequently in a data set. In this case, the number 177 appears twice, which is the most frequent number. Therefore, the data set has one mode, which is 177.
A survey of
9
adults employed full-time was taken. Here are their reported numbers of hours worked per week.
47
,
47
,
51
,
48
,
36
,
36
,
36
,
59
,
47
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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 a data set, we need to arrange the numbers in ascending order:
36, 36, 36, 47, 47, 47, 48, 51, 59
Since there are 9 numbers in the data set, the median is the middle number. In this case, the middle number is the 5th number, which is 47. Therefore, the median of this data set is 47.
(b) To find the mean of a data set, we need to sum up all the numbers and divide it by the total number of numbers.
Mean = (47 + 47 + 51 + 48 + 36 + 36 + 36 + 59 + 47) / 9 ≈ 397 / 9 ≈ 44.1
Therefore, the mean of this data set is approximately 44.1.
(c) A mode is the value that appears most frequently in a data set. In this case, the number 36 appears three times, which is the most frequent number. Therefore, the data set has one mode, which is 36.
An intelligence test was recently administered to a group of
7
people. Their respective completion times (in minutes) were as follows.
34
,
36
,
36
,
25
,
39
,
33
,
39
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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 a data set, we need to sum up all the numbers and divide it by the total number of numbers.
Mean = (34 + 36 + 36 + 25 + 39 + 33 + 39) / 7 = 242 / 7 ≈ 34.6
Therefore, the mean of this data set is approximately 34.6.
(b) To find the median of a data set, we need to arrange the numbers in ascending order:
25, 33, 34, 36, 36, 39, 39
Since there are 7 numbers in the data set, the median is the middle number. In this case, the middle number is the 4th and 5th numbers, which are 36 and 36. Therefore, the median of this data set is 36.
(c) A mode is the value that appears most frequently in a data set. In this case, the numbers 36 and 39 appear twice, which are the most frequent numbers. Therefore, the data set has two modes, which are 36 and 39.
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.
28
,
22
,
18
,
28
,
28
,
14
,
27
,
17
,
15
,
19
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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 a data set, we need to arrange the numbers in ascending order:
14, 15, 17, 18, 19, 22, 27, 28, 28, 28
Since there are 10 numbers in the data set, the median is the average of the two middle numbers. In this case, the two middle numbers are 19 and 22.
Median = (19 + 22) / 2 = 41 / 2 = 20.5
Therefore, the median of this data set is 20.5.
(b) To find the mean of a data set, we need to sum up all the numbers and divide it by the total number of numbers.
Mean = (28 + 22 + 18 + 28 + 28 + 14 + 27 + 17 + 15 + 19) / 10 = 236 / 10 = 23.6
Therefore, the mean of this data set is 23.6.
(c) A mode is the value that appears most frequently in a data set. In this case, the number 28 appears three times, which is the most frequent number. Therefore, the data set has one mode, which is 28.
To find the median of a data set, you need to arrange the numbers in ascending order and then find the middle value. If there is an even number of values, you will need to find the average of the two middle values.
First, let's arrange the numbers in ascending order:
-3, 2, 7, 11, 12, 15, 29, 30, 39
Since there are 9 values in total, the middle value will be the 5th number, which is 12. Therefore, the median of this data set is 12.
To find the mean (average) of a data set, you need to add up all the values and divide by the total number of values.
To calculate the mean, you can use the following formula:
Mean = (sum of all values) / (number of values)
Adding up all the values: -3 + 2 + 7 + 11 + 12 + 15 + 29 + 30 + 39 = 142
Dividing the sum by the number of values (9), we get: 142 / 9 = 15.8
Therefore, the mean of this data set is approximately 15.8.
To find the modes of a data set, you need to identify the value(s) that appear most frequently. A data set can have zero, one, or multiple modes.
In this case, there are no repeated values, so there are zero modes in this data set.
So, to summarize:
(a) The median of this data set is 12.
(b) The mean of this data set is approximately 15.8.
(c) There are zero modes in this data set.