Math Problem Statement

If we have the data:

5, 8, 15, 7, 10, 22, 3, 1, 15, 2

What is the median?

Solution

To find the median, we need to follow these steps:

  1. Arrange the data in ascending order: 1,2,3,5,7,8,10,15,15,221, 2, 3, 5, 7, 8, 10, 15, 15, 22

  2. Determine the number of data points: There are 10 values in total, which is an even number.

  3. Find the median:

    • For an even number of data points, the median is the average of the two middle numbers.
    • The middle numbers are the 5th and 6th values: 7 and 8.
  4. Calculate the average of the two middle values: 7+82=7.5\frac{7 + 8}{2} = 7.5

Therefore, the median is 7.5.

Would you like further details or clarification?

Here are some related questions you might find useful:

  1. How do you find the mode of this dataset?
  2. What is the range of this dataset?
  3. Can we calculate the mean of this dataset?
  4. How does the median differ from the mean?
  5. How do outliers affect the median?

Tip: The median is more resistant to outliers than the mean!

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Math Problem Analysis

Mathematical Concepts

Statistics
Median
Data Analysis

Formulas

Median for even number of data points: (n/2)th term + ((n/2) + 1)th term / 2

Theorems

Median theorem for even datasets

Suitable Grade Level

Grades 6-8