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Box and whisker diagram watch

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1. Hi all,

Im currently trying to revise for a maths skills test, and I'm looking at box and whisker diagrams. So far I've understood it, except one thing. I know the median is the middle value of a given data set, but what do you do if you are asked to draw a box and whisker diagram based on the following:
- The upper quartile
- The lower quartile
- The highest value
- The lowest value

How would you then work out (and apply to the diagram) the median? As I dont see any way of being able to tell how many values are in the data set, just from the information provided above.

I am looking at this website:
http://www.education.gov.uk/schools/...x-and-whiskers

Please explain this to me as I'm totally confused.

2. For dataset
2, 3, 5, 7, 9, 13, 15, 18, 19, 20, 22, 23

Q2-2 6-1
------=--------
23-2 12-1

Q2-2 5
------=------
21 11

Q2=11.5 (3 SF)
But it says there 14 is the median, so apart from extrapolation I'm not sure.
3. (Original post by krisshP)
For dataset
2, 3, 5, 7, 9, 13, 15, 18, 19, 20, 22, 23

Q2-2 6-1
------=--------
23-2 12-1

Q2-2 5
------=------
21 11

Q2=11.5 (3 SF)
But it says there 14 is the median, so apart from extrapolation I'm not sure.
I know how to work out the mediam when they give a data set, but how do you work it out when they dont give a data set?

If you scroll down the page of the link i pasted to where it says "Worked examples, Example one" they provide a table with values for the upper quartile, lower quartile, high score, and low score, for tests 1, 2, and 3, but thats all they provide. They dont give the data sets. And then if you look at the box and whisker diagrams underneath that, theyve shown the median for test 1,2,and 3, but i dont get how they worked it out (how they were able to mark where the median is for each of the tests) if there is no data set in which to work out the middle number...
4. (Original post by algyptalian91)
I know how to work out the mediam when they give a data set, but how do you work it out when they dont give a data set?

If you scroll down the page of the link i pasted to where it says "Worked examples, Example one" they provide a table with values for the upper quartile, lower quartile, high score, and low score, for tests 1, 2, and 3, but thats all they provide. They dont give the data sets. And then if you look at the box and whisker diagrams underneath that, theyve shown the median for test 1,2,and 3, but i dont get how they worked it out (how they were able to mark where the median is for each of the tests) if there is no data set in which to work out the middle number...
Not sure then, sorry.
5. (Original post by algyptalian91)
How would you then work out the median?
You can't. These notes are in error. Given only the four numbers supplied for each data set, it is impossible to find the median and hence impossible to draw the box plot.

Disappointing for a government website.
6. (Original post by profmatt)
You can't. These notes are in error. Given only the four numbers supplied for each data set, it is impossible to find the median and hence impossible to draw the box plot.

Disappointing for a government website.
Yeah I thought so too. Well thanks for confirming this!
7. (Original post by algyptalian91)
Hi all,

Im currently trying to revise for a maths skills test, and I'm looking at box and whisker diagrams. So far I've understood it, except one thing. I know the median is the middle value of a given data set, but what do you do if you are asked to draw a box and whisker diagram based on the following:
- The upper quartile
- The lower quartile
- The highest value
- The lowest value

How would you then work out (and apply to the diagram) the median? As I dont see any way of being able to tell how many values are in the data set, just from the information provided above.

I am looking at this website:
http://www.education.gov.uk/schools/...x-and-whiskers

Please explain this to me as I'm totally confused.

(Original post by profmatt)
You can't. These notes are in error. Given only the four numbers supplied for each data set, it is impossible to find the median and hence impossible to draw the box plot.

Disappointing for a government website.

Are we looking at different pages?

The link in the OP gives 20 values, the median lies half way between the 10th and 11th value
8. (Original post by TenOfThem)
Are we looking at different pages?

The link in the OP gives 20 values, the median lies half way between the 10th and 11th value
yeah its the same page but you're looking at the top section, my enquiry was regarding the second section, if you scroll down the page of the link i pasted to where it says "Worked examples, Example one" they provide a table with values for the upper quartile, lower quartile, high score, and low score, for tests 1, 2, and 3, but thats all they provide. They don't give the data sets. And then if you look at the box and whisker diagrams underneath that, theyve shown the median for test 1,2,and 3, so i was confused as to how they were able to mark where the median is for each of the tests if there is no data set in which to work out the middle number...
9. They haven't listed the median but they don't actually need to because they're not asking you to produce the box and whisker plot - just answer questions based on them. Indeed, in the last example they haven't even drawn on the median "for clarity" as it's not relevant to any of the questions.

If they'd asked you to draw the plots from the data sets then you wouldn't be able to. But that's not what they're asking you to do.

Posted from TSR Mobile
10. (Original post by seantnash)
They haven't listed the median but they don't actually need to because they're not asking you to produce the box and whisker plot - just answer questions based on them. Indeed, in the last example they haven't even drawn on the median "for clarity" as it's not relevant to any of the questions.

If they'd asked you to draw the plots from the data sets then you wouldn't be able to. But that's not what they're asking you to do.

Posted from TSR Mobile
They do ask you to produce the box and whisker plot on the data. Check the image. But I get it now, it's not possible to find the median without the full data set, that's the only confusion I had.

11. (Original post by seantnash)
They haven't listed the median but they don't actually need to because they're not asking you to produce the box and whisker plot - just answer questions based on them. Indeed, in the last example they haven't even drawn on the median "for clarity" as it's not relevant to any of the questions.

If they'd asked you to draw the plots from the data sets then you wouldn't be able to. But that's not what they're asking you to do.
With respect, that's exactly what they've asked. In the section headed "Worked examples" it says "The scores for the three tests are presented in the table below. Display this data using a box and whisker diagram." There then follows a table that excludes the median. After that it says "The box and whisker diagrams for each test are shown below" and these magically include the median.

This is clearly in error.
12. Oops you're absolutely right - I missed that bit of the blurb. Then you're right, it's definitely a screw up on their part.

Posted from TSR Mobile
13. Thanks a lot for the replies everyone. Definitely one less thing to worry about! :-)
14. Yes, no way to find the median, because we don't know what happen among the data within the Q3 and Q1 at all.
In fact this Box-plot is incorrect because Box-plot need to place the median as well!

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