Math Problem Statement

Which data set could be represented by the box plot shown below? A horizontal boxplot is plotted along a horizontal axis marked from 40 to 50, in increments of 1. A left whisker extends from 41 to 43. The box extends from 43 to 48 and is divided into 2 parts by a vertical line segment at 44. The right whisker extends from 48 to 50. All values estimated. Choose 1 answer: Choose 1 answer: (Choice A)
[41], [42], [43], [43], [43], [45], [47], [49], [50], [50] A [41], [42], [43], [43], [43], [45], [47], [49], [50], [50] (Choice B)
[41], [42], [42], [43], [43], [47], [47], [49], [50], [50] B [41], [42], [42], [43], [43], [47], [47], [49], [50], [50] (Choice C)
[40], [42], [43], [43], [43], [47], [47], [48], [50], [50] C [40], [42], [43], [43], [43], [47], [47], [48], [50], [50] (Choice D)
[41], [42], [43], [43], [43], [45], [47], [48], [50], [50] D [41], [42], [43], [43], [43], [45], [47], [48], [50], [50]

Solution

Let's break down the information from the box plot:

  • Left whisker: Extends from 41 to 43, so the minimum value is 41 and the first quartile (Q1) is near 43.
  • Box: The box spans from 43 to 48. The median (Q2) is at 44, which divides the box into two parts.
  • Right whisker: Extends from 48 to 50, meaning the maximum value is 50.

With this breakdown, let's evaluate each choice based on these insights.

Choice A:

4141, 4242, 4343, 4343, 4343, 4545, 4747, 4949, 5050, 5050

  • This set seems to have values that fit the range of the box plot, but the median would be at 44, not 43 as shown in this set.

Choice B:

4141, 4242, 4242, 4343, 4343, 4747, 4747, 4949, 5050, 5050

  • This set has a median of 43, but the box plot shows the median at 44, so this choice is incorrect.

Choice C:

4040, 4242, 4343, 4343, 4343, 4747, 4747, 4848, 5050, 5050

  • This set includes a minimum value of 40, but the whisker starts at 41 in the box plot, so this doesn't match.

Choice D:

4141, 4242, 4343, 4343, 4343, 4545, 4747, 4848, 5050, 5050

  • This set closely matches the given box plot: the whiskers start at 41 and extend to 50, with a median around 44.

Correct answer: Choice D.

Would you like a further breakdown of the box plot interpretation or any other details?


Here are some related questions to explore further:

  1. What is the significance of quartiles in a box plot?
  2. How do you calculate the median from a data set?
  3. What does the term "interquartile range" refer to in a box plot?
  4. How would outliers affect the interpretation of a box plot?
  5. How is a box plot different from a histogram in terms of data representation?

Tip: When looking at box plots, remember that the "box" shows the interquartile range (middle 50% of data), and the "whiskers" show the spread of the remaining data.

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Math Problem Analysis

Mathematical Concepts

Box Plot
Quartiles
Median
Data Visualization

Formulas

Median = middle value of the data set
Interquartile Range (IQR) = Q3 - Q1

Theorems

Properties of a Box Plot
Interpretation of Whiskers and Quartiles

Suitable Grade Level

Grades 6-8