Math Problem Statement
Find the 5 number summary for the data shown below.
92 46 48 79 98 49 77 29 38 33
5 number summary:
Incorrect, , ,
Solution
To compute the 5-number summary for the given data, we need to identify the following key values:
- Minimum: The smallest value in the dataset.
- First Quartile (Q1): The median of the lower half of the data (below the overall median).
- Median (Q2): The middle value of the dataset.
- Third Quartile (Q3): The median of the upper half of the data (above the overall median).
- Maximum: The largest value in the dataset.
Step-by-Step Calculation:
1. Arrange the data in ascending order:
2. Identify the 5-number summary:
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Minimum:
-
Maximum:
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Median (Q2): The median is the middle value of the dataset. Since there are 10 data points (even number), the median is the average of the 5th and 6th values:
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First Quartile (Q1): The lower half of the data is . The median of this subset is .
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Third Quartile (Q3): The upper half of the data is . The median of this subset is .
Final 5-Number Summary:
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Math Problem Analysis
Mathematical Concepts
Descriptive Statistics
Five-Number Summary
Quartiles
Formulas
Median = Middle value of sorted data or average of two middle values
Q1 = Median of the lower half of the data
Q3 = Median of the upper half of the data
Theorems
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Suitable Grade Level
Grades 6-8
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