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Given median of a five number

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Given median of a five number [#permalink] New post 28 Aug 2016, 03:17
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Given median of a five number set as 24.5. If a value k is added to each number in the set, then the new median becomes 28.5. What is the value of k?





[Reveal] Spoiler:
4

Last edited by Sonalika42 on 30 Aug 2016, 02:14, edited 1 time in total.
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Re: Given median of a five number [#permalink] New post 28 Aug 2016, 08:19
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Re: Given median of a five number [#permalink] New post 29 Aug 2016, 15:39
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Sonalika42 wrote:
Given median of a five number set as 24.5. If a value k is added to each number in the set, then the new median becomes 28.5. What is the value of k?


A quick approach to choose an initial set that satisfies the given condition.
Here's a 5-number set with a median of 24.5: {1, 2, 24.5, 27, 28}

Add k to each number in the set to get: {1+k, 2+k, 24.5+k, 27+k, 28+k}

As we can see, the median of the NEW SET is 24.5+k
Since we're told the new median is 28.5, we can write: 24.5+k = 28.5
Solve for k to get k = 4

Answer:
[Reveal] Spoiler:
4


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Re: Given median of a five number [#permalink] New post 19 Oct 2019, 00:42
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Hello,

A more algebraic approach would be to note the elements of the list as

a b c d e - the initial median is 24.5, which is equal to c in our case. So c=24.5

We are adding k to each element of the list
a b c d e | (+k)

Thus the set after this operation would be the following:
a+k b+k c+k d+k e+k

We can see from here that now the median is c+k, which is equal to 28.5
Now we have the system of equations:
c = 24.5
c+k = 28.5
From here we can see that k=4
Re: Given median of a five number   [#permalink] 19 Oct 2019, 00:42
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Given median of a five number

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