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graph above shows the frequency distribution of 50 integer

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GMAT Club Legend
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graph above shows the frequency distribution of 50 integer [#permalink] New post 12 Jan 2016, 17:09
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Question Stats:

65% (00:59) correct 34% (01:00) wrong based on 49 sessions
Image

The graph above shows the frequency distribution of 50 integer values varying from 1 to 6.

Quantity A
Quantity B
The average (arithmetic mean) of the 50 values
The median of the 50 values


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.




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Question: 5
Page: 458
Difficulty: medium/hard
[Reveal] Spoiler: OA

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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

CAT Tests
Re: graph above shows the frequency distribution of 50 integer [#permalink] New post 12 Jan 2016, 17:14
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Solution

In this question, you are given a graph of the frequency distribution of 50 integer values and are asked to compare the average (arithmetic mean) with the median of the distribution.

In general, the median of a group of n values, where n is even, is obtained by ordering the values from least to greatest and then calculating the average(arithmetic mean) of the two middle values. So, for the 50 values shown in the graph, the median is the average of the 25th and 26th values, both of which are equal to 5. Therefore, the median of the 50 values is 5.

Once you know that the median of the 50 values is 5, the comparison simplifies to comparing the average of the 50 values with 5. You can make this
comparison without actually calculating the average by noting from the graph that of the 50 values, 11 values are 1 unit above 5,
  • 16 values are equal to 5,
  • 10 values are 1 unit below 5, and
  • 13 values are more than 1 unit below 5.

Since the part of the distribution that is below 5 contains 23 values—13 of which are more than 1 unit below 5—and the part of the distribution that is above 5 contains 11 values—none of which is more than 1 unit above 5—the average (arithmetic mean) of the 50 values must be less than 5. The correct answer is Choice B.
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Re: graph above shows the frequency distribution of 50 integer [#permalink] New post 15 Mar 2018, 17:11
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Correct: B
Sum = 1 * 2 + 2 *4 + 3 * 7 + 4 * 10 + 5 * 16 + 6 * 11 = 217
Mean = Sum / total_number = Sum / 50 = 217 / 50 = 4.34

Median is the number that when we sort the numbers in an ascending order, it places exactly in the middle of sequence. Or if number of values is even, median is mean of two middle values. Here we should find the average of 25th and 26th values. By looking at the graph. We see 25th and 26th numbers have value 5, so the median is 5.

So median is bigger.

** Another way is that by looking in the graph we see 2 numbers having value 1, 4 numbers having 2, …, 10 numbers having 4. We know the middle numbers (25 and 26) are in 5. So median is 5. On the other hand for calculating the mean, while having median, we should be aware whether mean is bigger than median or not. So we should consider numbers more than 5 and numbers less than 5 for calculating mean. There are 11 numbers more than 5 and having the value 6. But in the left it seems there are more numbers having value less than 5. Of course if there were 11 numbers having a big value, we couldn’t deduce from the graph.
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Re: graph above shows the frequency distribution of 50 integer [#permalink] New post 24 Apr 2018, 19:06
For mean
11 values are greater than 5 and 23 values are less than 5 so it will bring mean less than 5
median will be avg of 25th and 26th term i.e 5+5/2 = 5
so clearly B>A
Re: graph above shows the frequency distribution of 50 integer   [#permalink] 24 Apr 2018, 19:06
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