Math Problem Statement
Sal counted the number of songs on each album in his collection. He created both a dot plot and a box plot to display the same data: A dot plot has a horizontal axis labeled, Number of songs, marked from 7 to 16 in increments of 1. The number of dots above each value is as follows. 7, 1; 8, 2; 9, 2; 10, 4; 11, 1; 12, 2; 13, 2; 14, 1; 15, 0; 16, 2. [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] A horizontal box plot is labeled, Number of songs, and marked from 7 to 16 in increments of 1. A left whisker extends from 7 to 9. The box extends from 9 to 13 and is divided into 2 parts by a vertical line segment at 10. The right whisker extends from 13 to 16. All values estimated. [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] Which display makes it easier to see that the median is [10] songs? Choose 1 answer: Choose 1 answer: (Choice A) The dot plot A The dot plot (Choice B) The box plot B The box plot Which display allows us to see that the mode is [10] songs? Choose 1 answer: Choose 1 answer: (Choice A) The dot plot A The dot plot (Choice B) The box plot B The box plot
Solution
To answer these questions, let's analyze the given information.
1. Which display makes it easier to see that the median is 10 songs?
- Box Plot: The median is typically represented by the vertical line inside the box. In the description provided, the box plot has a vertical line segment at 10, which clearly indicates that the median is 10 songs.
- Dot Plot: The dot plot shows the distribution of data points, but it doesn't directly show where the median lies. To find the median in a dot plot, you'd need to count and determine the middle value.
Answer: The box plot makes it easier to see that the median is 10 songs.
Correct Choice: B. The box plot
2. Which display allows us to see that the mode is 10 songs?
- Dot Plot: The mode is the value that appears most frequently. In the dot plot, you can see that 10 has the most dots above it (4 dots), indicating that the mode is 10.
- Box Plot: The box plot doesn't show the frequency of each value directly, so it's not possible to determine the mode just from the box plot.
Answer: The dot plot allows us to see that the mode is 10 songs.
Correct Choice: A. The dot plot
Would you like more details or have any questions? Here are some related questions:
- How can you find the median in a dot plot if it isn’t directly labeled?
- What other measures of central tendency are visible in a box plot?
- How does the range of the data set appear in both the dot plot and the box plot?
- What can the dot plot tell you about the data that the box plot cannot?
- Can a box plot show more than one mode?
- Why might someone prefer a dot plot over a box plot for small data sets?
- How would the appearance of the box plot change if the data were skewed?
- What is the significance of the whiskers in a box plot?
Tip: When analyzing data, use a box plot to quickly identify the median, quartiles, and potential outliers, while a dot plot is useful for seeing the distribution and frequency of individual data points.
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Math Problem Analysis
Mathematical Concepts
Statistics
Data Visualization
Measures of Central Tendency
Formulas
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Theorems
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Suitable Grade Level
Grades 6-8
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