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:
, , , , , , , , ,
- 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:
, , , , , , , , ,
- This set has a median of 43, but the box plot shows the median at 44, so this choice is incorrect.
Choice C:
, , , , , , , , ,
- 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:
, , , , , , , , ,
- 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:
- What is the significance of quartiles in a box plot?
- How do you calculate the median from a data set?
- What does the term "interquartile range" refer to in a box plot?
- How would outliers affect the interpretation of a box plot?
- 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