Math Problem Statement

Given the data set, {77, 72, 85, 66, 45, 63, 82}, identify the following values that would be used when creating the boxplot:

Highest Question Blank 1 of 5 type your answer...

Upper Quartile Question Blank 2 of 5 type your answer...

Median Question Blank 3 of 5 type your answer...

Lower Quartile Question Blank 4 of 5 type your answer...

Lowest Question Blank 5 of 5 type your answer...

Solution

To construct a boxplot from the data set {77, 72, 85, 66, 45, 63, 82}, we need to identify the following values:

Step 1: Arrange the data in ascending order.

The data set, when sorted, is: {45, 63, 66, 72, 77, 82, 85}

Step 2: Identify the required values.

  1. Highest (Maximum value):
    The highest value in the data set is 85.

  2. Upper Quartile (Q3):
    The upper quartile is the median of the upper half of the data (above the overall median).
    In the sorted data, the upper half is {77, 82, 85}. The median of this subset is 82.

  3. Median:
    The median is the middle value of the entire data set.
    Since there are 7 numbers, the middle value is the 4th one, which is 72.

  4. Lower Quartile (Q1):
    The lower quartile is the median of the lower half of the data (below the overall median).
    The lower half is {45, 63, 66}, and the median of this subset is 63.

  5. Lowest (Minimum value):
    The lowest value in the data set is 45.

Summary of values for the boxplot:

  • Highest: 85
  • Upper Quartile (Q3): 82
  • Median (Q2): 72
  • Lower Quartile (Q1): 63
  • Lowest: 45

Would you like more details on how these values are calculated or interpreted?


Here are 5 related questions for further understanding:

  1. How is the interquartile range (IQR) calculated from this data set?
  2. What would be considered an outlier in this data set based on the IQR?
  3. How does a boxplot represent data distribution?
  4. How would adding an additional data point affect the boxplot?
  5. What are the implications of a skewed boxplot?

Tip: The interquartile range (IQR) is a measure of spread and is calculated by subtracting the lower quartile (Q1) from the upper quartile (Q3).

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Math Problem Analysis

Mathematical Concepts

Statistics
Data Analysis
Quartiles
Boxplot

Formulas

Median of a data set
Quartile calculations (Q1, Q3)
Range (Maximum - Minimum)

Theorems

Quartile Calculation
Five-number Summary

Suitable Grade Level

Grades 6-8