Question

julia’s gym recorded the number of new members signups each month for 13 months. the box plot summarizes the results. which statement best describes the data represented in the box plot? a the mean number of new members is 11. b half the months had 43 to 65 new members. c the most new members in one month is 65. d the least new members in one month is 11.

Explanation:

Step1: Interpret box plot components

A box plot shows minimum, Q1, median, Q3, maximum. From the plot: min=20, Q1=31, median=41, Q3=49, max=65.

Step2: Evaluate each option

• Option A: Median is 41, not mean. Incorrect.
• Option B: Q3=49, max=65. The top 25% of months (not half) are 49-65. Incorrect.
• Option C: Maximum is 65, not the "most" (mode, unstated). Incorrect.
• Option D: Minimum value is 20, not 31. Wait, correction: Recheck plot: the left whisker ends at 20, Q1 is 31. Wait, no—reassess D: The lowest new members is 20? No, wait, no, let's recheck options again. Wait, no: Option B: Half the months are between Q1 and Q3? No, Q1 to Q3 is 50% of data. Wait, Q1=31, Q3=49? No, the box plot: the box starts at 31, median at 41, ends at 49. Whiskers: left to 20, right to 65.

Wait, Option B says "Half the months had 49 to 65 new members"—no, 49 to 65 is top 25%. Option D: "The lowest new members in one month is 31"—no, lowest is 20. Wait, no, wait I misread. Wait, no: Option B correction: Wait, 50% of data is between Q1 and Q3 (31 to 49). Option C: The maximum is 65, but "most" refers to mode, which we can't get from box plot. Option A: Mean is not shown, median is 41. Wait, no—wait the correct option is: Wait, no, let's re-express:
Wait, Option D: No, lowest is 20. Option B is wrong. Wait, wait, maybe I misread the plot. Wait, the left whisker is at 20, Q1 is 31, median 41, Q3 49, right whisker 65.
Wait, Option B: "Half the months had 49 to 65"—no, that's 25%. Option A: Median is 41, not mean. Option C: "The most new members in one month is 65"—that is correct, because 65 is the maximum value (highest number of new members in a single month). Oh! I misread option C: it says "the most new members in one month is 65"—that is the maximum, which is correct. Option D says lowest is 31, which is wrong (lowest is 20).

Step3: Confirm correct option

Option C states the maximum value, which matches the box plot's right whisker (65).

Answer:

C. The most new members in one month is 65.