A certain streaming-music website allows users to rate songs with an integer number of stars from 1 to 5. The...

Owning The Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

1. The median rating is 4 stars, because the cumulative percentage of ratings reaches 50% at the 4-star band \(\mathrm{(32.7\% + 25.0\% = 57.7\%)}\).
2. About 7,500 users gave Song X a 4-star rating \(\mathrm{(25.0\% \times 29,984 = 7,496)}\), which rounds to 7,500).
3. The rating distribution is polarized: over half the users (57.7%) gave high marks (4 or 5 stars), but nearly one in five gave just 1 star, and neutral 3-star and mid-low 2-star ratings are less common.

Step-by-Step Solution

Question 1: Identifying the Median Star Rating

Complete Statement:

The median number of stars given to Song X by all users who rated it was ______

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: median number of stars
  • Meaning: The value that separates the higher half from the lower half of all ratings when sorted.
  • Relation to Chart: We must determine what rating corresponds to the middle (median) user in the ordered data of all star ratings.
  • Important Implications: Requires understanding the cumulative distribution of users' star ratings.

• Statement Breakdown 2:
  • Key Phrase: all users who rated it
  • Meaning: Every user who has left a rating on Song X.
  • Relation to Chart: The entirety of the percentages (totaling 100%) represent all such users.
  • Important Implications: All percentages and counts are to be based off the full population of raters.

• What is needed: Which star rating includes the 14,992nd and 14,993rd ratings when all 29,984 ratings are sorted from lowest to highest.

Solution:

• Condensed Solution Implementation:
  Sum the percentages of ratings from lowest to highest to see where the median falls.
• Necessary Data points:
  Total ratings: 29,984. Distribution: 5 stars: 32.7%, 4 stars: 25.0%, 3 stars: 14.9%, 2 stars: 9.0%, 1 star: 18.4%.
  • Calculations Estimations:
    Cumulative up to 1 star: 18.4%. Up to 2 stars: 27.4%. Up to 3 stars: 42.3%. Up to 4 stars: 67.3%. 42.3% of users gave 3 stars or fewer. The 50% point is crossed in the 4-star group.
  • Comparison to Answer Choices:
    Options: 2, 3, 4. '4' is the only correct answer because the 4-star group contains the median.

FINAL ANSWER Blank 1: 4

Question 2: Number of Users Who Gave the Median Rating

Complete Statement:

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

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: total of ______ users
  • Meaning: Find the count that corresponds to the median rating group calculated before.
  • Relation to Chart: The pie chart's percentages can be converted to counts using the total number of users.

• Statement Breakdown 2:
  • Key Phrase: gave Song X that number of stars
  • Meaning: Users who gave exactly four stars, since 4 was found as the median.
  • Relation to Chart: The percentage for the 4-star group is 25.0%, which should be multiplied by the total user count.

• What is needed: How many users out of 29,984 gave Song X a 4-star rating, rounded to the nearest hundred.

Solution:

• Condensed Solution Implementation:
  Find 25% of 29,984 and round to the nearest hundred.
• Necessary Data points:
  Total users: 29,984. 4-star percentage: 25.0%.
  • Calculations Estimations:
    \(\mathrm{29,984 \times 0.25 = 7,496}\) users. Rounded to the nearest hundred: 7,500.
  • Comparison to Answer Choices:
    Options: 2,700, 4,500, 7,500. '7,500' is the correct choice.

FINAL ANSWER Blank 2: 7,500

Summary

The median number of stars is 4 because the cumulative percentage crosses 50% within the 4-star group. 25% of 29,984 users is 7,496, which rounds up to 7,500. Therefore, the answers are 4 and 7,500.

Question Independence Analysis

Blank 2 depends on Blank 1: you need to know what rating was the median (from Blank 1) before you can determine how many users gave that rating (Blank 2). Thus the blanks are dependent.