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 Post subject: Maths question - averages using algebra?Posted: Sun Jul 05, 2020 9:55 am

Joined: Thu Oct 18, 2012 10:41 am
Posts: 482
Hello,

Please could someone help with the following question:

The mean weight of 5 children is 45kg.
The mean weight of the lightest three children is 42kg and the mean weight of
the heaviest three children is 49kg.
What is the median weight of the children in kg?

I've managed to answer it using 3 different algebraic equations and substitution, but DS would find this approach too complicated.
Is there another way to answer this?

Thanks

PS taken from an 11+ sample paper

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 Post subject: Re: Maths question - averages using algebra?Posted: Sun Jul 05, 2020 10:40 am

Joined: Sun Mar 17, 2019 8:56 am
Posts: 197
Hi,
Sorry I can’t help with the maths but as far as I am aware only the mean is covered on the KS2 national curriculum. If you are needing to use algebraic equations to solve it then I would suggest this question is beyond the level of the 11+. My child sat the 11+ last year- the 11+ practice maths book (Bond) was far beyond what had been taught at school and the feedback after the test was that it was far easier than the Bond book and was stuff done at school.

My advice, for what it’s worth, is to not worry about this sort of question (it’s unlike to come up and will only be worth a couple of points if it does). Do concentrate on times tables; speed and accuracy with completing MCQs; and making sure your child is secure with the areas covered on the KS2 maths curriculum.

I’m sure someone mathematically minded will be along to help with your question though!

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 Post subject: Re: Maths question - averages using algebra?Posted: Sun Jul 05, 2020 10:47 am

Joined: Mon Feb 12, 2007 2:21 pm
Posts: 16254

The mean weight of 5 children is 45kg.
The mean weight of the lightest three children is 42kg and the mean weight of the heaviest three children is 49kg.
What is the median weight of the children in kg?

PS taken from an 11+ sample paper

What is the total weight of all 5 children?

What is the total weight of the lightest 3? Heaviest 3?

How can we use these to get the median? [this is *not* a suitable 11+ question]

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 Post subject: Re: Maths question - averages using algebra?Posted: Sun Jul 05, 2020 2:00 pm

Joined: Mon Jun 18, 2007 3:32 pm
Posts: 7675
Location: East Kent
Median, mode and range are not part of KS2 curriculum any more (unless the curriculum has changed again since I retired -it's even harder keeping up with it once you've left the chalk face!)

Algebra in KS2 is fairly simple just using and deriving simple equations and expressions so I would not expect a child who has is just at the beginning of year 6 to use algebra to solve this.

It might be fun to have a go at it, using G55's hints, but I would not worry too much about this type of question as it is unlikely to come up in the real thing. Out of interest what paper was this, was there a date?

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 Post subject: Re: Maths question - averages using algebra?Posted: Sun Jul 05, 2020 3:42 pm

Joined: Mon Feb 12, 2007 2:21 pm
Posts: 16254
Finding the mean is in Year 6 but not the median.

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 Post subject: Re: Maths question - averages using algebra?Posted: Sun Jul 05, 2020 3:46 pm

Joined: Mon Jun 18, 2007 3:32 pm
Posts: 7675
Location: East Kent
The question was from a 2008 paper which explains why median was included.

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 Post subject: Re: Maths question - averages using algebra?Posted: Mon Jul 06, 2020 9:48 pm

Joined: Sun Aug 19, 2018 4:57 pm
Posts: 165
I would explain it as follows:

You have children A, B, C, D, E (in weight order). The weight of child C will be the median. Their total weight is 5x45 = 225kg

Children A, B, C have a combined weight of 126kg (42x3)
Children C, D, E have a combined weight of 147kg (49X3)
Add them together child A, B, C, C, D, E= 273kg
273- 225 = 48kg (weight of child C)

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 Post subject: Re: Maths question - averages using algebra?Posted: Tue Aug 25, 2020 6:21 pm

Joined: Wed Sep 18, 2019 2:57 pm
Posts: 30
You can use the principle of Venn Diagram which is well within the KS2 syllabus.
Each circle in the Venn Diagram should represent the higher total and lower total respectively. The overlapping section in the middle is then the median. Each circle is (49*3) and (42*3) respectively and the sum of all is (45*5).

Should be easy to work out from there.

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 Post subject: Re: Maths question - averages using algebra?Posted: Tue Aug 25, 2020 7:17 pm

Joined: Sun Mar 17, 2019 8:56 am
Posts: 197
BabaPabz wrote:
You can use the principle of Venn Diagram which is well within the KS2 syllabus.

Venn diagrams are introduced in the KS3 curriculum so this, along with the median, should not be an 11+ question.

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 Post subject: Re: Maths question - averages using algebra?Posted: Wed Aug 26, 2020 8:52 am

Joined: Wed Sep 18, 2019 2:57 pm
Posts: 30
Nella, Strangely enough you are right at least according to the national curriculum===>

https://www.gov.uk/government/publicati ... s-of-study

I said strangely because,..... Venn diagram questions were in every 11+ exams that my son did last academic year for super selective state and private schools. Even my daughter now in Year4 has been introduced to the concept at school. Perhaps they call it something else in KS2. you will find lots of Venn diagram questions in standard 11+ textbooks.

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