Math Problem Statement
The data below represents the number of practices each member of Nidhi's ski team attended. [25], [28], [29], [29], [30], [34], [35], [35], [37], [38] Which box plot correctly summarizes the data? Choose 1 answer: Choose 1 answer: (Choice A) A horizontal boxplot is plotted along a horizontal axis marked from 24 to 40, in increments of 1. A left whisker extends from 25 to 29. The box extends from 29 to 35 and is divided into 2 parts by a vertical line segment at 34. The right whisker extends from 35 to 38. All values estimated. A A horizontal boxplot is plotted along a horizontal axis marked from 24 to 40, in increments of 1. A left whisker extends from 25 to 29. The box extends from 29 to 35 and is divided into 2 parts by a vertical line segment at 34. The right whisker extends from 35 to 38. All values estimated. (Choice B) A horizontal boxplot is plotted along a horizontal axis marked from 24 to 40, in increments of 1. A left whisker extends from 25 to 29. The box extends from 29 to 35 and is divided into 2 parts by a vertical line segment at 30. The right whisker extends from 35 to 38. All values estimated. B A horizontal boxplot is plotted along a horizontal axis marked from 24 to 40, in increments of 1. A left whisker extends from 25 to 29. The box extends from 29 to 35 and is divided into 2 parts by a vertical line segment at 30. The right whisker extends from 35 to 38. All values estimated. (Choice C) A horizontal boxplot is plotted along a horizontal axis marked from 24 to 40, in increments of 1. A left whisker extends from 25 to 29. The box extends from 29 to 35 and is divided into 2 parts by a vertical line segment at 32. The right whisker extends from 35 to 38. All values estimated. C A horizontal boxplot is plotted along a horizontal axis marked from 24 to 40, in increments of 1. A left whisker extends from 25 to 29. The box extends from 29 to 35 and is divided into 2 parts by a vertical line segment at 32. The right whisker extends from 35 to 38. All values estimated.
Solution
To determine which box plot correctly summarizes the data, let's go through the process of creating a box plot step by step.
Step 1: Organize the Data
The data set is:
Step 2: Calculate Key Statistics
To make a box plot, we need the following five statistics:
- Minimum: The smallest value in the dataset, which is 25.
- First Quartile (Q1): The median of the lower half of the data.
- Lower half of the data:
- The median of this subset is 29, so .
- Median (Q2): The median of the entire dataset.
- The full dataset:
- The median is the average of the two middle values: , so .
- Third Quartile (Q3): The median of the upper half of the data.
- Upper half of the data:
- The median of this subset is 35, so .
- Maximum: The largest value in the dataset, which is 38.
Step 3: Create the Box Plot
From the data:
- The minimum is 25.
- The first quartile is 29.
- The median is 32.
- The third quartile is 35.
- The maximum is 38.
Now, let’s review the boxplot choices:
- Choice A has a vertical line at 34 (which is incorrect, as the median is 32).
- Choice B has a vertical line at 30 (which is incorrect, as the median is 32).
- Choice C has a vertical line at 32 (which is correct, as the median is 32).
Conclusion:
The correct box plot is Choice C.
Let me know if you'd like more details on this process or have any questions!
Related questions:
- How do you calculate the quartiles for an odd number of data points?
- What is the difference between the first and third quartile?
- How can you find the median in a dataset with an even number of data points?
- How does the interquartile range (IQR) help in identifying outliers in a dataset?
- What is the significance of the whiskers in a box plot?
Tip:
To avoid errors when reading box plots, always double-check that the vertical line inside the box correctly matches the median of your dataset!
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Math Problem Analysis
Mathematical Concepts
Box Plots
Quartiles
Median
Interquartile Range
Formulas
Q1 = Median of lower half
Q2 = Median of the data set
Q3 = Median of upper half
Theorems
Interquartile Range (IQR) helps identify spread of data
Suitable Grade Level
Grades 6-8