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The table shown above has distribution of test scores. Which score interval contains the median of the 73 scores?

A. 60-69 B. 70-79 C. 80-89 D. 90-99 E. Cannot be determined.

Please explain your answer.

Median of 73 data points is the middle term - 37rd score. First 3 score ranges cover total of 28 scores (2+10+16), 37rd will be in fourth range (it covers scores from 80 to 89).

Re: The table above shows the distribution of test scores for a [#permalink]

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23 May 2014, 23:26

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stne wrote:

we are asked to find the median of the 73 scores, which is the 37th term.

Now if we arrange the number of scores( not score intervals ) in ascending order as shown below which is what we do when we want to calculate the median of a number of terms:the Median term 37th falls in the 90-99 interval.

Confused as to , why we shouldn't arrange the frequency ( no. of scores in a particular interval ) in ascending order when calculating the Median.

Hi Stne, To find median of test-scores,we have to arrange them in an order (ascending or descending) and find the middle term.Now,the middle term is 37 th term in the order.

For the score distribution ,one can add one more column Cumulative frequency

SCORE INTERVAL---------NUMBER OF SCORES --------- Cumulative Frequency

We can see arranging the scores in ascending, shows first 28 test scores are below 80. Next 27 scores , i.e. 29th,30th,....,37th,......,55th score appear in SCORE INTERVAL 80-89. So median is in interval 80-89. Hope it helps.

The table shown above has distribution of test scores. Which score interval contains the median of the 73 scores?

A. 60-69 B. 70-79 C. 80-89 D. 90-99 E. Cannot be determined.

Please explain your answer.

Median of 73 data points is the middle term - 37rd score. First 3 score ranges cover total of 28 scores (2+10+16), 37rd will be in fourth range (it covers scores from 80 to 89).

Answer: C.

Dear Bunnel, As I know, the arrangement either in ascending or in descending order is a must in case of finding median. So, it would be 2+10+16+18+27. By adding 2+10+16 we get 28. Then, we need to add 18 and we get 46. So, 37 comes within 46 and the range should be 90-99 as it is the range for 18. Kindly tell me where I missed.

I think you misinterpreted the question. We have that there are: 2 scores from 50-59, say both are 55; 10 scores from 60-69, say all are 65; 16 scores from 70-79, say all are 75; 27 scores from 80-89, say all are 85; 18 scores from 90-99, say all are 95.

Re: The table above shows the distribution of test scores for a [#permalink]

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21 Feb 2015, 19:20

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Median is the "middle value" when all the data are arranged in ascending/descending order. For example, if the data is:

3,4,7,9, 87 -> Median is 7 (middle value).

Notice that there were 5 data points above, and the middle value is the 3rd value.

Here, there are 73 data points and so, the middle value will be 37th value. So, we just have to find out that 37th value will lie in which score interval.

2 values are lesser than 59 12 (2+10) values are lesser than 69 28 (2+10+16) values are lesser than 79 55 (2+10+16+27) values are lesser than 89

So, if 28 values are lesser than 79 and 55 values are lesser than 89

In this question, what is the value of data? Is it counted as 1 or 9?

50-59 is counted as 1 or 9? Even though the value of mean is not asked I wanted to calculate it but I don't know what sum to take.

We are given the range of the values here. The actual values can be "51 and 52" or "58 and 59" So, we cannot calculate the mean in this case.
_________________

Re: The table above shows the distribution of test scores for a [#permalink]

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09 Nov 2012, 06:47

we are asked to find the median of the 73 scores, which is the 37th term.

Now if we arrange the number of scores( not score intervals ) in ascending order as shown below which is what we do when we want to calculate the median of a number of terms:the Median term 37th falls in the 90-99 interval.

Confused as to , why we shouldn't arrange the frequency ( no. of scores in a particular interval ) in ascending order when calculating the Median.

Re: The table above shows the distribution of test scores for a [#permalink]

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23 May 2014, 13:04

Even I have the same question. I too followed this method and got the interval 90-99

Any help here?

stne wrote:

we are asked to find the median of the 73 scores, which is the 37th term.

Now if we arrange the number of scores( not score intervals ) in ascending order as shown below which is what we do when we want to calculate the median of a number of terms:the Median term 37th falls in the 90-99 interval.

Confused as to , why we shouldn't arrange the frequency ( no. of scores in a particular interval ) in ascending order when calculating the Median.

Re: The table above shows the distribution of test scores for a [#permalink]

Show Tags

24 Sep 2014, 22:18

gmatacequants wrote:

stne wrote:

we are asked to find the median of the 73 scores, which is the 37th term.

Now if we arrange the number of scores( not score intervals ) in ascending order as shown below which is what we do when we want to calculate the median of a number of terms:the Median term 37th falls in the 90-99 interval.

Confused as to , why we shouldn't arrange the frequency ( no. of scores in a particular interval ) in ascending order when calculating the Median.

Hi Stne, To find median of test-scores,we have to arrange them in an order (ascending or descending) and find the middle term.Now,the middle term is 37 th term in the order.

For the score distribution ,one can add one more column Cumulative frequency

SCORE INTERVAL---------NUMBER OF SCORES --------- Cumulative Frequency

We can see arranging the scores in ascending, shows first 28 test scores are below 80. Next 27 scores , i.e. 29th,30th,....,37th,......,55th score appear in SCORE INTERVAL 80-89. So median is in interval 80-89. Hope it helps.

The table shown above has distribution of test scores. Which score interval contains the median of the 73 scores?

A. 60-69 B. 70-79 C. 80-89 D. 90-99 E. Cannot be determined.

Please explain your answer.

Median of 73 data points is the middle term - 37rd score. First 3 score ranges cover total of 28 scores (2+10+16), 37rd will be in fourth range (it covers scores from 80 to 89).

Answer: C.

Dear Bunnel, As I know, the arrangement either in ascending or in descending order is a must in case of finding median. So, it would be 2+10+16+18+27. By adding 2+10+16 we get 28. Then, we need to add 18 and we get 46. So, 37 comes within 46 and the range should be 90-99 as it is the range for 18. Kindly tell me where I missed.

Re: The table above shows the distribution of test scores for a [#permalink]

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12 Aug 2015, 03:51

Can someone please explain me in prcise details what is the meaning of the the question? I have a hard time understanding the actual question like what do they mean by distribution by interval how is range coming here etc? Thanks a million.

Can someone please explain me in prcise details what is the meaning of the the question? I have a hard time understanding the actual question like what do they mean by distribution by interval how is range coming here etc? Thanks a million.

You are asked to find the median value and median of a set is the middle most value (for odd number of elements) in a set in which all elements are ordered either in increasing or in decreasing order.

For this question, we will focus on the increasing nature of the elements.

As the total number of elements = 73, an odd number, the median will be the 37th term. So you need to find in what interval will be 37th lie in

From the data set provided, you have 2 people in 50-59 range, 10 people in 60-69 etc.

Thus if you have to write the set , you will get the following method

50-59, 50-59, 60-69, 60-69 (repeat 8 more times), 70-79 (16 times), 80-89 (27 times) and 90-99 (18 times).

Thus, the 37th term will be after 2 for 50-59, 10 of 60-69 , 16 of 70-79 and 9 of 80-89 for a total of 2+10+16+9 = 37.

Thus the median value will lie in the interval 80-89. C is the correct answer.
_________________

What does it mean 2 people in 50-59 range, 10 people in 60-69

It means that 2 people are in the range 50-59, i.e. 2 people have a score that is in the range 50-59 and similarly 10 people have a score that is in the range 60-69 etc.
_________________

The table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 73 scores?

A. 60-69 B. 70-79 C. 80-89 D. 90-99 E. It cannot be determined from the information given.

Median of a set with odd number of elements = the middle element of the set if arranged in ascending/descending order. Median of a set with even number of elements = average of middle two numbers if arranged in ascending/descending order.

In the given case, total elements = 2 + 10 + 16 + 27 + 18 = 73 = 36 + 1 + 36 Hence the median will be the 37th term. The 37th term will lie in the range 80 - 89

Re: The table above shows the distribution of test scores for a [#permalink]

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10 Dec 2016, 21:44

Below solution is more clear.

Median of 73 scores must be the 37th score when all the scores are arranged in increasing or decreasing order. In the score interval 50-79 there are (2 + 10 + 16) = 28 scores. Hence the 37-th score is not in this interval.

But in the score interval 50-89 there are (2 + 10 + 16 + 27) = 55 scores. Hence the 37-th score is in the score interval 80-89.

The correct answer is C.
_________________

Thanks & Regards, Anaira Mitch

gmatclubot

Re: The table above shows the distribution of test scores for a
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10 Dec 2016, 21:44

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