A certain streaming-music website allows users to rate songs with an

Question

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A certain streaming-music website allows users to rate songs with an integer number of stars from 1 to 5. The graph shows, for each number of stars, among all 29,984 users who rated Song X, the percent who gave it that number of stars. Each of those users rated the song exactly once.

Select from the drop-down menus the options that create the statement that most accurately reflects the information provided.

The median number of stars given to Song X by all users who rated it was  GRAPH_1_PLACEHOLDER , and a total of  GRAPH_2_PLACEHOLDER  users gave Song X that number of stars, to the nearest hundred users.

ID: 700363

Bunuel · Accepted Answer

Let's consider an easier example where 20 users rated Song X:

20%, or 4 users, gave  1 star ; 
 15%, or 3 users, gave  2 stars ; 
 10%, or 2 users, gave  3 stars ; 
 30%, or 6 users, gave  4 stars ; 
 25%, or 5 users, gave  5 stars .

Arranging the ratings in ascending order:

1, 1, 1, 1,   2, 2, 2,   3, 3,    4, 4,    4, 4, 4, 4,   5, 5, 5, 5, 5

The median is the average of the two middle terms: (4 + 4)/2 = 4.

swaftnishant · Answer

in my opinion answer should be 1 star as it will come on 3rd number when we'll arrange these from smallest to largest?

guddo · Answer

Here is the OE from the OG: https://gmatclub.com/forum/download/file.php?id=82793 GMAT-Club-Forum-1k160jgz.png

Taresh23 · Answer

Does this mean that the ratings are lined up in increasing order and whichever rating is coming in 50th percent of the voted rating is taken as median? GMAT-Club-Forum-udjeyczz.png

Bunuel · Answer

Yes. The median of a list of values is the middle value for an odd number of values and the average of the two middle values for an even number of values, that is when the values are arranged in order . GMAT-Club-Forum-gzm3l2a0.png

Sneha2021 · Answer

Bunuel   KarishmaB

How to decide order of the values to find median?

We can find median "when the values are arranged in order" but i was confused how the values should be arranged in this case.

One way is based on star rating and 3 star will be the median
1 star, 2 star,3 star, 4 & 5

Another way is list the order of % and find the corresponding star as median
%. - 9, 15, 18, 25 & 33
Star - 3, 2, 1, 4, 5

can you help me understand the medain concept in this case?

Thanks!

nust2017 · Answer

A video explanation of this question would be super helpful!

MintTea · Answer

As the median is the middle value in ascending or descending order. we list it from 1 start to 5 stars or vice versa from 5 stars to 1 stars. In another word, find the value fall into 50% group

We see that 4 starts takes the middle value of 50% => 4 stars

Arjun123321 · Answer

I think it depends upon how the question is asked. If it says median of STARS, arrange stars from 1-5 according to respective percentage. Howevr, if question asked median of "PERCENTAGE" values, then arrange according to increasing percentage values of 9, 15, 18, 25 and 33.

soma7 · Answer

its easy....star 1 is 18.4% star 2 is 14.9% and star 3 is 9%....so total is 42.3%....the balance 7.7% comes under star 4 to get the 50th percentage value as the median.

nabeelfarooqui · Answer

From the pie chart (total users = 29,984), the percentage distribution by stars is:
 • 1 star: 18.4%
 • 2 stars: 14.9%
 • 3 stars: 9.0%
 • 4 stars: 25.0%
 • 5 stars: 32.7%
These sum to 100%.
1) Median number of stars
Sort ratings from 1→5 and compute cumulative percentages:
 • Up to 1 star: 18.4%
 • Up to 2 stars: 18.4%+14.9%=33.3%
 • Up to 3 stars: 33.3%+9.0%=42.3%
 • Up to 4 stars: 42.3%+25.0%=67.3%
 • Up to 5 stars: 100%
The median lies at the 50th percentile. The cumulative crosses 50% within the 4-star group (goes from 42.3% to 67.3%). Therefore, the median rating is 4 stars.
2) Number of users who gave the median rating (nearest hundred)
Users giving 4 stars = 25.0% of 29,984.
0.25 × 29,984 = 7,496 users → to the nearest hundred ≈ 7,500 users.
Final
 • Median stars: 4
 • Number of users at the median rating (nearest hundred): 7,500

dhruva09 · Answer

Bunuel  I took me 3.54 mins to solve this question correctly. Can you suggest shorthand method to solve this quicker. 
ps: I took rounded value of 30000 while solving it in that time.

A certain streaming-music website allows users to rate songs with an

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