Math Is Fun Forum

popsyclover

Member

Registered: 2011-02-06

Posts: 6

Mean, Median and Range

I have a puzzle and I am having problems working out a simple way with the following:
Find 5 numbers that have a range of 5, a median of 16 and a mean of 15.  How do I work out simply the 5 numbers with the median being 16 to total 75?  Thanks so much for any advice

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mean, Median and Range

Hi popsyclover;

There are many solutions to solve that set of conditions. Can you restrict them a little more?

First of all, when you say numbers do you mean whole numbers. Do you mean positive numbers. Do you want the smallest set of numbers? Do they have to be 5 different numbers?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

popsyclover

Member

Registered: 2011-02-06

Posts: 6

Re: Mean, Median and Range

Hi bobbym - thanks for replying!  Unfortunately the question set for homework (Key Stage 2) literally only states "Find 5 numbers that have a range of 5, a median of 16 and a mean of 15".

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mean, Median and Range

Hi;

Your grade?

There are 3 solutions for positive numbers. But siome will have to be the same.

Call the numbers a,b,c,d,e with a <= b <= c <= d <= e

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

popsyclover

Member

Registered: 2011-02-06

Posts: 6

Re: Mean, Median and Range

Hi,

Im in the UK and I'm 10 years old, and currently in year 6.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mean, Median and Range

Hi;

Welcome to the forum. Your teacher set you a very difficult task and needs to learn a little rigor in how he/she phrases questions. Check the post above for 3 solutions.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Mean, Median and Range

hi popsyclover

I think there is more than one answer. 

I drew 5 boxes and put 16 in the middle.

Then I filled in with 4 numbers above and below 16.

Then I juggled the numbers until the other conditions were met.

Here's an answer:

12,  13.1,  16,  16.9,  17

You could change the numbers by making 13.1 bigger and 16.9 smaller by the same amount.

For key stage 2 I would expect whole numbers so I'll look some more.

Bob

Last edited by Bob (2011-02-06 09:36:47)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

popsyclover

Member

Registered: 2011-02-06

Posts: 6

Re: Mean, Median and Range

Thank you so much for your help! I have tried all eveing at this, and will try to battle on with the rest of the questions!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mean, Median and Range

Hi;

There are only 3 integer solutions. See the above post #4. At your level only trial and error is possible.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Mean, Median and Range

Nope.  Cannot do it.

So either repeat as bobbym suggests or use decimals as I suggest.

Or really impress your teacher by giving lots of possibilities ! 

bobbym.  There use to be key stage 2 tests.  I think they have been abolished now but I'm a bit out of touch.  The Government website says it's all under revision (new Government: announce sweeping reforms ...).  I expect the wording was straight from an old test, and pity the poor marker who has to check every different answer to see if it works.  On second thoughts; why pity, they get paid for it!

Bob

Last edited by Bob (2011-02-06 09:48:22)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mean, Median and Range

Or, you can politely tell your teacher that he/she should learn how to phrase questions better so that they have solutions for young students to discover. Perhaps if he/she were a member of this forum...

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

popsyclover

Member

Registered: 2011-02-06

Posts: 6

Re: Mean, Median and Range

Hi guys - thanks so much for the help and for trying to put yourselves in my position!   Best wishes.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Mean, Median and Range

and don't spend ages on a question.  Ask for help here; we love it :)

post 10 revised.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mean, Median and Range

Hi popsyclover;

Pick one of the answers given and use that. Come back if you need help with anything.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

popsyclover

Member

Registered: 2011-02-06

Posts: 6

Re: Mean, Median and Range

I will certainly use one of those answers, and thank you so much for your help! You guys are so nice! :)