A set having the same mean, median, mode, and range
Is it possible to have a set with the same mean, median, mode, and range?
If not, how can the following question be solved:
Set $H$ contains five positive integers such that the mean, median,
mode, and range are all equal. The sum of the data is $25$.
Using the above information, indicate which one will be greater:
a) the smallest possible number in set $H$.
b) 6.
If I assume that all the elements in set $H$ are equal to $5$, it doesn't satisfy the conditions for range, as the range will become zero then.
statistics means median
edited Jun 5 '15 at 4:36
Ken
3,60151728
asked Jun 5 '15 at 4:17
India Slaver
27118
add a comment |
Is it possible to have a set with the same mean, median, mode, and range?
If not, how can the following question be solved:
Set $H$ contains five positive integers such that the mean, median,
mode, and range are all equal. The sum of the data is $25$.
Using the above information, indicate which one will be greater:
a) the smallest possible number in set $H$.
b) 6.
If I assume that all the elements in set $H$ are equal to $5$, it doesn't satisfy the conditions for range, as the range will become zero then.
statistics means median
edited Jun 5 '15 at 4:36
Ken
3,60151728
asked Jun 5 '15 at 4:17
India Slaver
27118
The list ${0,0}$ works quite well for you first question.
– Mike Pierce
Jun 5 '15 at 4:26
@MikePierce Serious suggestion ?
– callculus
Jun 5 '15 at 4:33
add a comment |
Is it possible to have a set with the same mean, median, mode, and range?
If not, how can the following question be solved:
Set $H$ contains five positive integers such that the mean, median,
mode, and range are all equal. The sum of the data is $25$.
Using the above information, indicate which one will be greater:
a) the smallest possible number in set $H$.
b) 6.
If I assume that all the elements in set $H$ are equal to $5$, it doesn't satisfy the conditions for range, as the range will become zero then.
statistics means median
edited Jun 5 '15 at 4:36
Ken
3,60151728
asked Jun 5 '15 at 4:17
India Slaver
27118
Is it possible to have a set with the same mean, median, mode, and range?
If not, how can the following question be solved:
Set $H$ contains five positive integers such that the mean, median,
mode, and range are all equal. The sum of the data is $25$.
Using the above information, indicate which one will be greater:
a) the smallest possible number in set $H$.
b) 6.
If I assume that all the elements in set $H$ are equal to $5$, it doesn't satisfy the conditions for range, as the range will become zero then.
statistics means median
statistics means median
edited Jun 5 '15 at 4:36
Ken
3,60151728
asked Jun 5 '15 at 4:17
India Slaver
27118
edited Jun 5 '15 at 4:36
Ken
3,60151728
asked Jun 5 '15 at 4:17
India Slaver
27118
edited Jun 5 '15 at 4:36
Ken
3,60151728
edited Jun 5 '15 at 4:36
Ken
3,60151728
edited Jun 5 '15 at 4:36
Ken
3,60151728
3,60151728
asked Jun 5 '15 at 4:17
India Slaver
27118
asked Jun 5 '15 at 4:17
India Slaver
27118
asked Jun 5 '15 at 4:17
India Slaver
27118
27118
The list ${0,0}$ works quite well for you first question.
– Mike Pierce
Jun 5 '15 at 4:26
@MikePierce Serious suggestion ?
– callculus
Jun 5 '15 at 4:33
add a comment |
The list ${0,0}$ works quite well for you first question.
– Mike Pierce
Jun 5 '15 at 4:26
@MikePierce Serious suggestion ?
– callculus
Jun 5 '15 at 4:33
The list ${0,0}$ works quite well for you first question.
– Mike Pierce
Jun 5 '15 at 4:26
The list ${0,0}$ works quite well for you first question.
– Mike Pierce
Jun 5 '15 at 4:26
@MikePierce Serious suggestion ?
– callculus
Jun 5 '15 at 4:33
@MikePierce Serious suggestion ?
– callculus
Jun 5 '15 at 4:33
add a comment |
2 Answers
2
active
oldest
votes
The multiset $[3, 4, 5, 5, 8]$ will fit the bill.
You know, though, that even if you didn't have an example of a set on hand, the smallest element must be less than or equal to $5$ since the median is $5$ (since the mean is $5$).
answered Jun 5 '15 at 4:31
Ken
3,60151728
Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
– India Slaver
Jun 5 '15 at 4:35
add a comment |
Hint: If I allow non-integers and let the set contain duplicates (I think duplicates are allowed, though generally a set does not allow them. To have a mode you need duplicates), ${2.5,5,5,5,7.5}$ satisfies the constraints. Can you modify it to use only integers?
answered Jun 5 '15 at 4:27
Ross Millikan
291k23196370
add a comment |
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2 Answers
2
active
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2 Answers
2
active
oldest
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oldest
votes
The multiset $[3, 4, 5, 5, 8]$ will fit the bill.
You know, though, that even if you didn't have an example of a set on hand, the smallest element must be less than or equal to $5$ since the median is $5$ (since the mean is $5$).
answered Jun 5 '15 at 4:31
Ken
3,60151728
Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
– India Slaver
Jun 5 '15 at 4:35
add a comment |
The multiset $[3, 4, 5, 5, 8]$ will fit the bill.
You know, though, that even if you didn't have an example of a set on hand, the smallest element must be less than or equal to $5$ since the median is $5$ (since the mean is $5$).
answered Jun 5 '15 at 4:31
Ken
3,60151728
Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
– India Slaver
Jun 5 '15 at 4:35
add a comment |
The multiset $[3, 4, 5, 5, 8]$ will fit the bill.
You know, though, that even if you didn't have an example of a set on hand, the smallest element must be less than or equal to $5$ since the median is $5$ (since the mean is $5$).
answered Jun 5 '15 at 4:31
Ken
3,60151728
The multiset $[3, 4, 5, 5, 8]$ will fit the bill.
You know, though, that even if you didn't have an example of a set on hand, the smallest element must be less than or equal to $5$ since the median is $5$ (since the mean is $5$).
answered Jun 5 '15 at 4:31
Ken
3,60151728
answered Jun 5 '15 at 4:31
Ken
3,60151728
answered Jun 5 '15 at 4:31
Ken
3,60151728
answered Jun 5 '15 at 4:31
Ken
3,60151728
3,60151728
Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
– India Slaver
Jun 5 '15 at 4:35
add a comment |
Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
– India Slaver
Jun 5 '15 at 4:35
Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
– India Slaver
Jun 5 '15 at 4:35
Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
– India Slaver
Jun 5 '15 at 4:35
add a comment |
Hint: If I allow non-integers and let the set contain duplicates (I think duplicates are allowed, though generally a set does not allow them. To have a mode you need duplicates), ${2.5,5,5,5,7.5}$ satisfies the constraints. Can you modify it to use only integers?
answered Jun 5 '15 at 4:27
Ross Millikan
291k23196370
add a comment |
Hint: If I allow non-integers and let the set contain duplicates (I think duplicates are allowed, though generally a set does not allow them. To have a mode you need duplicates), ${2.5,5,5,5,7.5}$ satisfies the constraints. Can you modify it to use only integers?
answered Jun 5 '15 at 4:27
Ross Millikan
291k23196370
add a comment |
Hint: If I allow non-integers and let the set contain duplicates (I think duplicates are allowed, though generally a set does not allow them. To have a mode you need duplicates), ${2.5,5,5,5,7.5}$ satisfies the constraints. Can you modify it to use only integers?
answered Jun 5 '15 at 4:27
Ross Millikan
291k23196370
Hint: If I allow non-integers and let the set contain duplicates (I think duplicates are allowed, though generally a set does not allow them. To have a mode you need duplicates), ${2.5,5,5,5,7.5}$ satisfies the constraints. Can you modify it to use only integers?
answered Jun 5 '15 at 4:27
Ross Millikan
291k23196370
answered Jun 5 '15 at 4:27
Ross Millikan
291k23196370
answered Jun 5 '15 at 4:27
Ross Millikan
291k23196370
answered Jun 5 '15 at 4:27
Ross Millikan
291k23196370
291k23196370
add a comment |
add a comment |
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The list ${0,0}$ works quite well for you first question.
– Mike Pierce
Jun 5 '15 at 4:26
@MikePierce Serious suggestion ?
– callculus
Jun 5 '15 at 4:33