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.
-
Highest (Maximum value):
The highest value in the data set is 85. -
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. -
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. -
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. -
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:
- How is the interquartile range (IQR) calculated from this data set?
- What would be considered an outlier in this data set based on the IQR?
- How does a boxplot represent data distribution?
- How would adding an additional data point affect the boxplot?
- 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
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