the data set represents the total number of pencils each student in a class needs to sharpen.\n0, 1, 1, 1…

the data set represents the total number of pencils each student in a class needs to sharpen.\n0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9\nwhich box plot correctly represents the data?

the data set represents the total number of pencils each student in a class needs to sharpen.\n0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9\nwhich box plot correctly represents the data?

Answer

Explanation:

Step1: Find the minimum, Q1, median, Q3, maximum

The data set is (0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9) (11 values).

  • Minimum (( \text{min} )): (0)
  • Q1 (25th percentile): The median of the first 5 values ((0, 1, 1, 1, 2)) is (1).
  • Median (50th percentile): The 6th value is (3).
  • Q3 (75th percentile): The median of the last 5 values ((4, 4, 6, 6, 9)) is (6).
  • Maximum (( \text{max} )): (9)

Step2: Analyze the box plot components

A box plot has:

  • Whisker from min ((0)) to Q1 ((1)),
  • Box from Q1 ((1)) to Q3 ((6)), with median ((3)) inside,
  • Whisker from Q3 ((6)) to max ((9)).

Now, check the plots:

  • The first plot: Min=0, Q1=1, median=3, Q3=6, max=9 (matches our calculations).

Answer:

The first box plot (with min=0, Q1=1, median=3, Q3=6, max=9) correctly represents the data. (Assuming the first plot’s whiskers and box align with these values.)