Mixing
(Box and Whisker Plot Problem) Why is the answer choice 3 instead of choice 2?
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Problem #$6$ has me confused. The answer key of the textbook I am using states that the answer is choice $3$. But shouldn't the answer be choice $2$ ( $7$ students ) because the numbers, $81$ through $88$, are below Q$3$?
statistics
edited Jul 30 at 4:51
高田航
1,116318
asked Jul 30 at 3:40
AniJan
113
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up vote
0
down vote
favorite
(Look at the link below)
Problem #$6$ has me confused. The answer key of the textbook I am using states that the answer is choice $3$. But shouldn't the answer be choice $2$ ( $7$ students ) because the numbers, $81$ through $88$, are below Q$3$?
statistics
edited Jul 30 at 4:51
高田航
1,116318
asked Jul 30 at 3:40
AniJan
113
I believe you are correct: the given range is between the median and the 3rd quartile, which contains $1/4$ of the students.
– angryavian
Jul 30 at 3:42
The question in the book is not well put (see my answer below). A possible meaningful question would be "AT LEAST how many students scored from 81 to 88?" Then, you can derive the answer 7 by applying the properties of the quartiles as follows: AT LEAST 14 scores ($50%$ of the scores) must be greater than or equal to the second quartile (the median). AT MOST 7 scores ($25%$ of the scores) can be greater than the third quartile (assumed to be 88). So, AT LEAST 7 students scored from 81 to 88.
– trancelocation
Jul 31 at 6:23
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
(Look at the link below)
Problem #$6$ has me confused. The answer key of the textbook I am using states that the answer is choice $3$. But shouldn't the answer be choice $2$ ( $7$ students ) because the numbers, $81$ through $88$, are below Q$3$?
statistics
edited Jul 30 at 4:51
高田航
1,116318
asked Jul 30 at 3:40
AniJan
113
(Look at the link below)
Problem #$6$ has me confused. The answer key of the textbook I am using states that the answer is choice $3$. But shouldn't the answer be choice $2$ ( $7$ students ) because the numbers, $81$ through $88$, are below Q$3$?
statistics
edited Jul 30 at 4:51
高田航
1,116318
asked Jul 30 at 3:40
AniJan
113
edited Jul 30 at 4:51
高田航
1,116318
edited Jul 30 at 4:51
高田航
1,116318
edited Jul 30 at 4:51
高田航
1,116318
1,116318
asked Jul 30 at 3:40
AniJan
113
asked Jul 30 at 3:40
AniJan
113
asked Jul 30 at 3:40
AniJan
113
113
I believe you are correct: the given range is between the median and the 3rd quartile, which contains $1/4$ of the students.
– angryavian
Jul 30 at 3:42
The question in the book is not well put (see my answer below). A possible meaningful question would be "AT LEAST how many students scored from 81 to 88?" Then, you can derive the answer 7 by applying the properties of the quartiles as follows: AT LEAST 14 scores ($50%$ of the scores) must be greater than or equal to the second quartile (the median). AT MOST 7 scores ($25%$ of the scores) can be greater than the third quartile (assumed to be 88). So, AT LEAST 7 students scored from 81 to 88.
– trancelocation
Jul 31 at 6:23
add a comment |Â
I believe you are correct: the given range is between the median and the 3rd quartile, which contains $1/4$ of the students.
– angryavian
Jul 30 at 3:42
The question in the book is not well put (see my answer below). A possible meaningful question would be "AT LEAST how many students scored from 81 to 88?" Then, you can derive the answer 7 by applying the properties of the quartiles as follows: AT LEAST 14 scores ($50%$ of the scores) must be greater than or equal to the second quartile (the median). AT MOST 7 scores ($25%$ of the scores) can be greater than the third quartile (assumed to be 88). So, AT LEAST 7 students scored from 81 to 88.
– trancelocation
Jul 31 at 6:23
I believe you are correct: the given range is between the median and the 3rd quartile, which contains $1/4$ of the students.
– angryavian
Jul 30 at 3:42
I believe you are correct: the given range is between the median and the 3rd quartile, which contains $1/4$ of the students.
– angryavian
Jul 30 at 3:42
The question in the book is not well put (see my answer below). A possible meaningful question would be "AT LEAST how many students scored from 81 to 88?" Then, you can derive the answer 7 by applying the properties of the quartiles as follows: AT LEAST 14 scores ($50%$ of the scores) must be greater than or equal to the second quartile (the median). AT MOST 7 scores ($25%$ of the scores) can be greater than the third quartile (assumed to be 88). So, AT LEAST 7 students scored from 81 to 88.
– trancelocation
Jul 31 at 6:23
The question in the book is not well put (see my answer below). A possible meaningful question would be "AT LEAST how many students scored from 81 to 88?" Then, you can derive the answer 7 by applying the properties of the quartiles as follows: AT LEAST 14 scores ($50%$ of the scores) must be greater than or equal to the second quartile (the median). AT MOST 7 scores ($25%$ of the scores) can be greater than the third quartile (assumed to be 88). So, AT LEAST 7 students scored from 81 to 88.
– trancelocation
Jul 31 at 6:23
add a comment |Â
2 Answers
2
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up vote
3
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Yes, you are correct. The plot shows that the median ($2$nd quartile) is $81$, and that the $3$rd quartile is at $88$, so this range should contain exactly $28(0.25)=7$ students.
answered Jul 30 at 3:45
高田航
1,116318
add a comment |Â
up vote
1
down vote
The question cannot be answered from the given box plot.
Example:
Any ordered score set for $28$ students of the following type would produce the same box plot:
(I have difficulty to read the $Q_3$ from your picture, so I assume it to be $Q_3= 88$.)
$$beginpmatrix
Place: & 1 & cdots & 7 & 8 & cdots & 14 & 15 & cdots & 21 & 22 & cdots & 28 \
Score: & 62 & cdots & 71 & 71 & cdots & 81 & 81 & cdots & 88 & 88 & cdots & 92
endpmatrix$$
This would give possible numbers of scores from 81 to 88 ranging from 9 to 19.
If we assume that $Q_3 = fracx_21+x_222$, then consider the follwoing score set:
$$beginpmatrix
Place: & 1 & cdots & 7 & 8 & cdots & 14 & 15 & cdots & 21 & 22 & cdots & 28 \
Score: & 62 & cdots & 71 & 71 & cdots & 80 & 82 & cdots & 87 & 89 & cdots & 92
endpmatrix$$
This would give the answer of 7 scores ranging from 81 to 88.
answered Jul 30 at 7:45
trancelocation
4,5701413
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
Yes, you are correct. The plot shows that the median ($2$nd quartile) is $81$, and that the $3$rd quartile is at $88$, so this range should contain exactly $28(0.25)=7$ students.
answered Jul 30 at 3:45
高田航
1,116318
add a comment |Â
up vote
3
down vote
Yes, you are correct. The plot shows that the median ($2$nd quartile) is $81$, and that the $3$rd quartile is at $88$, so this range should contain exactly $28(0.25)=7$ students.
answered Jul 30 at 3:45
高田航
1,116318
add a comment |Â
up vote
3
down vote
up vote
3
down vote
Yes, you are correct. The plot shows that the median ($2$nd quartile) is $81$, and that the $3$rd quartile is at $88$, so this range should contain exactly $28(0.25)=7$ students.
answered Jul 30 at 3:45
高田航
1,116318
Yes, you are correct. The plot shows that the median ($2$nd quartile) is $81$, and that the $3$rd quartile is at $88$, so this range should contain exactly $28(0.25)=7$ students.
answered Jul 30 at 3:45
高田航
1,116318
answered Jul 30 at 3:45
高田航
1,116318
answered Jul 30 at 3:45
高田航
1,116318
answered Jul 30 at 3:45
高田航
1,116318
1,116318
add a comment |Â
add a comment |Â
up vote
1
down vote
The question cannot be answered from the given box plot.
Example:
Any ordered score set for $28$ students of the following type would produce the same box plot:
(I have difficulty to read the $Q_3$ from your picture, so I assume it to be $Q_3= 88$.)
$$beginpmatrix
Place: & 1 & cdots & 7 & 8 & cdots & 14 & 15 & cdots & 21 & 22 & cdots & 28 \
Score: & 62 & cdots & 71 & 71 & cdots & 81 & 81 & cdots & 88 & 88 & cdots & 92
endpmatrix$$
This would give possible numbers of scores from 81 to 88 ranging from 9 to 19.
If we assume that $Q_3 = fracx_21+x_222$, then consider the follwoing score set:
$$beginpmatrix
Place: & 1 & cdots & 7 & 8 & cdots & 14 & 15 & cdots & 21 & 22 & cdots & 28 \
Score: & 62 & cdots & 71 & 71 & cdots & 80 & 82 & cdots & 87 & 89 & cdots & 92
endpmatrix$$
This would give the answer of 7 scores ranging from 81 to 88.
answered Jul 30 at 7:45
trancelocation
4,5701413
add a comment |Â
up vote
1
down vote
The question cannot be answered from the given box plot.
Example:
Any ordered score set for $28$ students of the following type would produce the same box plot:
(I have difficulty to read the $Q_3$ from your picture, so I assume it to be $Q_3= 88$.)
$$beginpmatrix
Place: & 1 & cdots & 7 & 8 & cdots & 14 & 15 & cdots & 21 & 22 & cdots & 28 \
Score: & 62 & cdots & 71 & 71 & cdots & 81 & 81 & cdots & 88 & 88 & cdots & 92
endpmatrix$$
This would give possible numbers of scores from 81 to 88 ranging from 9 to 19.
If we assume that $Q_3 = fracx_21+x_222$, then consider the follwoing score set:
$$beginpmatrix
Place: & 1 & cdots & 7 & 8 & cdots & 14 & 15 & cdots & 21 & 22 & cdots & 28 \
Score: & 62 & cdots & 71 & 71 & cdots & 80 & 82 & cdots & 87 & 89 & cdots & 92
endpmatrix$$
This would give the answer of 7 scores ranging from 81 to 88.
answered Jul 30 at 7:45
trancelocation
4,5701413
add a comment |Â
up vote
1
down vote
up vote
1
down vote
The question cannot be answered from the given box plot.
Example:
Any ordered score set for $28$ students of the following type would produce the same box plot:
(I have difficulty to read the $Q_3$ from your picture, so I assume it to be $Q_3= 88$.)
$$beginpmatrix
Place: & 1 & cdots & 7 & 8 & cdots & 14 & 15 & cdots & 21 & 22 & cdots & 28 \
Score: & 62 & cdots & 71 & 71 & cdots & 81 & 81 & cdots & 88 & 88 & cdots & 92
endpmatrix$$
This would give possible numbers of scores from 81 to 88 ranging from 9 to 19.
If we assume that $Q_3 = fracx_21+x_222$, then consider the follwoing score set:
$$beginpmatrix
Place: & 1 & cdots & 7 & 8 & cdots & 14 & 15 & cdots & 21 & 22 & cdots & 28 \
Score: & 62 & cdots & 71 & 71 & cdots & 80 & 82 & cdots & 87 & 89 & cdots & 92
endpmatrix$$
This would give the answer of 7 scores ranging from 81 to 88.
answered Jul 30 at 7:45
trancelocation
4,5701413
The question cannot be answered from the given box plot.
Example:
Any ordered score set for $28$ students of the following type would produce the same box plot:
(I have difficulty to read the $Q_3$ from your picture, so I assume it to be $Q_3= 88$.)
$$beginpmatrix
Place: & 1 & cdots & 7 & 8 & cdots & 14 & 15 & cdots & 21 & 22 & cdots & 28 \
Score: & 62 & cdots & 71 & 71 & cdots & 81 & 81 & cdots & 88 & 88 & cdots & 92
endpmatrix$$
This would give possible numbers of scores from 81 to 88 ranging from 9 to 19.
If we assume that $Q_3 = fracx_21+x_222$, then consider the follwoing score set:
$$beginpmatrix
Place: & 1 & cdots & 7 & 8 & cdots & 14 & 15 & cdots & 21 & 22 & cdots & 28 \
Score: & 62 & cdots & 71 & 71 & cdots & 80 & 82 & cdots & 87 & 89 & cdots & 92
endpmatrix$$
This would give the answer of 7 scores ranging from 81 to 88.
answered Jul 30 at 7:45
trancelocation
4,5701413
answered Jul 30 at 7:45
trancelocation
4,5701413
answered Jul 30 at 7:45
trancelocation
4,5701413
answered Jul 30 at 7:45
trancelocation
4,5701413
4,5701413
add a comment |Â
add a comment |Â
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I believe you are correct: the given range is between the median and the 3rd quartile, which contains $1/4$ of the students.
– angryavian
Jul 30 at 3:42
The question in the book is not well put (see my answer below). A possible meaningful question would be "AT LEAST how many students scored from 81 to 88?" Then, you can derive the answer 7 by applying the properties of the quartiles as follows: AT LEAST 14 scores ($50%$ of the scores) must be greater than or equal to the second quartile (the median). AT MOST 7 scores ($25%$ of the scores) can be greater than the third quartile (assumed to be 88). So, AT LEAST 7 students scored from 81 to 88.
– trancelocation
Jul 31 at 6:23