Math Problem Statement

The box-and-whisker plot below represents some data set. What percentage of the data values are less than or equal to 75?

Solution

This is a box-and-whisker plot, and it shows how data is distributed across quartiles. To answer the question about what percentage of data values are less than or equal to 75, we need to understand where 75 falls on the plot.

From the image:

  • The left whisker starts around 10.
  • The left end of the box (the first quartile, Q1) is around 30.
  • The middle line of the box (the median, Q2) is approximately 50.
  • The right end of the box (the third quartile, Q3) is about 75.
  • The right whisker ends near 100.

Key Point:

The value of 75 corresponds to the third quartile (Q3), which means 75% of the data is less than or equal to 75.

So, the answer is 75%.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

  1. What percentage of the data is greater than 75?
  2. What is the interquartile range (IQR) of this data set?
  3. What percentage of the data is below the median (50)?
  4. How would you interpret a value in the left whisker region (between 10 and 30)?
  5. What would the box-and-whisker plot look like if the median were closer to 30?

Tip: In box plots, the median and quartiles divide the data into four equal parts, making it easy to understand percentages.

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Math Problem Analysis

Mathematical Concepts

Statistics
Data Distribution
Box-and-Whisker Plot
Quartiles

Formulas

Percentage formula
Quartiles definition

Theorems

Quartile theorem
Box plot interpretation

Suitable Grade Level

Grades 6-8