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Find value of a variable a set of numbers knowing its median and mean

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Find value of a variable a set of numbers knowing its median and mean  [#permalink]

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New post Updated on: 14 Jan 2019, 16:26
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In a hot dog eating contest, there were 13 contestants. The median of the number of hot dogs eaten was 10 and the arithmetic mean was 17. What is the minimum value of hot dogs eaten by the winner?

Originally posted by Luanaisa on 11 Jan 2019, 12:36.
Last edited by Luanaisa on 14 Jan 2019, 16:26, edited 1 time in total.
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Re: Find value of a variable a set of numbers knowing its median and mean  [#permalink]

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New post 11 Jan 2019, 14:34
Please check the Rules for Posting to provide proper questions

https://gmatclub.com/forum/rules-for-po ... 33935.html
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Re: Find value of a variable a set of numbers knowing its median and mean  [#permalink]

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New post 11 Jan 2019, 17:19
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C7= 10
(6*10+10+6x)/13=17
6x+70= 17*13
6x+70= 170+51=221
6x=221-70
6x=151
X= 151/6

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Re: Find value of a variable a set of numbers knowing its median and mean  [#permalink]

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New post 11 Jan 2019, 20:21
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In a hot dog eating contest, there were 13 contestants. The median of the number of hot dogs eaten was 10 and the arithmetic mean was 17. How many hot dogs have the winner eaten

I think you are missing a part of the question, it should be like what are the maximum number or minimum number of hot dogs the winner has eaten.. OR each contestant had different number of hot dogs..
We can only conclude that winner will have eaten more number of hot dogs, nothing about the other contestant count, except that they are less than the winner count and one or all of the first can have median count and remaining 7 we can't find..
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Re: Find value of a variable a set of numbers knowing its median and mean  [#permalink]

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New post 14 Jan 2019, 16:28
I have changed the question adding the minimum amount for the winner. I took a test that had this question, but I didn't knew how to solve it.
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Re: Find value of a variable a set of numbers knowing its median and mean  [#permalink]

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New post 14 Jan 2019, 18:00
to figure our the minimum hot dogs eaten by winner, consider below.
10, 10, 10, 10, 10, 10 10, x, x, x , x, x, x+1
We know that mean is 17 and median is 10
Now 17*13- 10*7 -1 = 6x
x= 150/6
= 25 is correct answer.
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Re: Find value of a variable a set of numbers knowing its median and mean  [#permalink]

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New post 14 Jan 2019, 18:33
So, inorder to have a minimum number of hot dogs, we have to increase the weightage of all the number of hotdogs eaten by the different participants.
But we can't have 10+ below the median (13+1)/2 = 7th highest hot dogs eaten
We consider first 7 participants count as 10
And as said we can now increase the weightage of the remaining except the winner to x and as the winner should have eaten more number of hot dogs compared to other, let it be x+1

So, (10*7 + 5*x + x+1)/13 = 17
6x = 150
x = 25
Minimum number of hotdogs a winner can have among 13 participants with mean 17 = 25
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Re: Find value of a variable a set of numbers knowing its median and mean   [#permalink] 14 Jan 2019, 18:33
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