The table shows the frequency distribution of the random variable X.

Question

https://gmatclub.com/forum/download/file.php?id=41585 The table shows the frequency distribution of the random variable X. What is the median of the distribution of the values of X ? A. 1.0 B. 1.8 C. 2.0 D. 2.5 E. 3.0 table.jpg

Madhavi1990 · Answer

Approach:
0 appears 6 times, 1 appears 11 times, 2 appears 18 times, 3 appears 23 times, 4 appears 15 times
so 2's and 3's appear the most. 
Hence the median should be 2.5

Will wait for OA

DavidTutorexamPAL · Answer

The median value has half of the values above it and half below it.
We'll write things out so we can SEE the answer, an Alternative approach.

Arranging all the numbers in order:
First 6 numbers are 0
Another 11 numbers, that is numbers 7 to 17 are 1
Next 18 numbers, that is numbers 18 to 35 are 2
Next 23 numbers, that is numbers 36 to 58 are 3
Next 15 numbers, that is numbers 59 to 73 are 4.

So, since there are 73 numbers the median is the 36th number which is 3.

(E) is our answer.

EgmatQuantExpert · Answer

Solution

Given:  
 • The table provides the frequency distribution of the random variable x

To find:  
 • The median of the distribution of the values of x

Approach and Working:   
In a given distribution, median denotes the middle-most value or the average of the two middle values, when arranged in ascending or descending order.
 • Total number of terms present in the distribution of x = 6 + 11 + 18 + 23 + 15 = 73

As 73 is odd, the median will be the 37th term

Now, if the values are arranged in ascending order,
 • Terms 1 to 6: 0
• Terms 7 to 17: 1
• Terms 18 to 35: 2
• Terms 36 to 58: 3
• Terms 59 to 73: 4

We can see 37th term will be equal to 3, which is the median of the distribution

Hence, the correct answer is option E.

Answer: E

jackspire · Answer

Hello Madhavi,
We derive a Median by finding out the middle term of a sequence written in an ascending order.
Here, the sum of total frequency is 73. So, the median will be the 37th term itself.

The answer would have been 2.5 if the total frequency would have been an even number i.e. 72 for example and the 36th term was 2 and the 37th term was 3.

Please feel free to ask if you didn't get my thought process.
Not an expert.

PKN · Answer

From the frequency distribution table, Cumulative frequency=73

So, there are 74 elements in the set X.

Median of the set=  \frac{(73+1)}{2} th term in the set X=37th term

From the table,

37th term =3 (when X=3, cumulative frequency=58 and it's frequency range is 36-58)

Ans option (E)

GynCliff · Answer

For me I will take it this way...

Since we're trying to find the middle number when all elements are arranged is descending/ascending order, 
I will use the frequency and cancel out the elements.

So six 0s will cancel out with six 4s

Then the remaining nine 4s will cancel out nine 1s.

Then the remaining two 1s will cancel out with two 3s remaining me with 21 3s and 18 2s

the 18 2s will cancel out with 18 3s then I remain with three 3s AND THE MEDIAN OF THREE 3S IS = ??

Answer E (in less than 30s)

bumpbot · Answer

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The table shows the frequency distribution of the random variable X.

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The table shows the frequency distribution of the random variable X.

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