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555-605 (Medium)|   Graphs|   Math Related|         
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guddo
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A certain streaming-music website allows users to rate songs with an 19 Aug 2024, 03:06
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Dropdown 1: 4 Dropdown 2: 7,500
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78% (01:58) correct 22% (02:40) wrong based on 1865 sessions

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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 , and a total of users gave Song X that number of stars, to the nearest hundred users.

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ID: 700363
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Bunuel
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A certain streaming-music website allows users to rate songs with an 04 Sep 2024, 00:21
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Sneha2021
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!
Show more
­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.­
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swaftnishant
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in my opinion answer should be 1 star as it will come on 3rd number when we'll arrange these from smallest to largest?
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guddo
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swaftnishant
in my opinion answer should be 1 star as it will come on 3rd number when we'll arrange these from smallest to largest?
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­
Here is the OE from the OG:


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guddo

swaftnishant
in my opinion answer should be 1 star as it will come on 3rd number when we'll arrange these from smallest to largest?
­
Here is the OE from the OG:

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­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?
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Bunuel
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A certain streaming-music website allows users to rate songs with an 23 Aug 2024, 08:46
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Taresh23

guddo

swaftnishant
in my opinion answer should be 1 star as it will come on 3rd number when we'll arrange these from smallest to largest?
­
Here is the OE from the OG:

­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?
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­
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.
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Sneha2021
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A certain streaming-music website allows users to rate songs with an 04 Sep 2024, 00:08
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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!
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soma7
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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.
Bunuel
Sneha2021
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!
­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.­
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swaftnishant
in my opinion answer should be 1 star as it will come on 3rd number when we'll arrange these from smallest to largest?
Show more
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
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