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:

  1. Minimum: The smallest value in the dataset.
  2. First Quartile (Q1): The median of the lower half of the data (below the overall median).
  3. Median (Q2): The middle value of the dataset.
  4. Third Quartile (Q3): The median of the upper half of the data (above the overall median).
  5. Maximum: The largest value in the dataset.

Step-by-Step Calculation:

1. Arrange the data in ascending order:

29,33,38,46,48,49,77,79,92,9829, 33, 38, 46, 48, 49, 77, 79, 92, 98

2. Identify the 5-number summary:

  • Minimum: 2929

  • Maximum: 9898

  • 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: Median=48+492=48.5\text{Median} = \frac{48 + 49}{2} = 48.5

  • First Quartile (Q1): The lower half of the data is 29,33,38,46,4829, 33, 38, 46, 48. The median of this subset is 3838.

  • Third Quartile (Q3): The upper half of the data is 49,77,79,92,9849, 77, 79, 92, 98. The median of this subset is 7979.

Final 5-Number Summary:

Minimum: 29,Q1: 38,Median (Q2): 48.5,Q3: 79,Maximum: 98\text{Minimum: } 29, \quad \text{Q1: } 38, \quad \text{Median (Q2): } 48.5, \quad \text{Q3: } 79, \quad \text{Maximum: } 98

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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