Math Problem Statement
Solution
Let's begin by finding the five-number summary for the given data set:
Data:
3, 8, 8, 5, 2, 9, 8, 7, 9, 6, 9, 4, 1, 6, 2, 9, 8, 7, 7, 9
First, we will sort the data in ascending order:
1, 2, 2, 3, 4, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9
Now, we can calculate the five-number summary:
-
Minimum (Min): The smallest value in the data set.
-
First Quartile (Q1): The median of the lower half of the data (excluding the median if the number of data points is odd). The lower half of the data is: The median of this half (Q1) is:
-
Median (Q2): The middle value of the entire data set. The median of the full data set is:
-
Third Quartile (Q3): The median of the upper half of the data. The upper half of the data is: The median of this half (Q3) is:
-
Maximum (Max): The largest value in the data set.
The five-number summary is:
- Min = 1
- Q1 = 5.5
- Median (Q2) = 7
- Q3 = 8
- Max = 9
Box-and-Whisker Plot:
Based on this summary, you can now choose the correct box-and-whisker plot. From the choices (A or B), I would need more context to determine which one is correct based on their labels. However, you can check which one shows:
- The minimum at 1,
- The lower quartile at 5.5,
- The median at 7,
- The upper quartile at 8,
- And the maximum at 9.
Let me know if you want further details or if you have any questions.
Here are five related questions to expand on this topic:
- How do you calculate interquartile range (IQR) using the five-number summary?
- What does the box in the box-and-whisker plot represent?
- How do outliers affect the box-and-whisker plot?
- What are the advantages of using a box-and-whisker plot for data representation?
- How do you interpret the spread of data from a box-and-whisker plot?
Tip:
When calculating the quartiles, always ensure the data is sorted in ascending order before determining the median and quartiles.
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Math Problem Analysis
Mathematical Concepts
Descriptive Statistics
Quartiles
Box-and-Whisker Plot
Formulas
Five-number summary
Quartiles
Median
Theorems
The concept of quartiles and interquartile range
Suitable Grade Level
Grades 8-10
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