Math Problem Statement

What is the median of the following data set? {17, 24, 18, 14, 20, 28, 30, 18}

Solution

To find the median of the given data set:

The data set provided is: 17,24,18,14,20,28,30,1817, 24, 18, 14, 20, 28, 30, 18

Step 1: Sort the data in ascending order.

14,17,18,18,20,24,28,3014, 17, 18, 18, 20, 24, 28, 30

Step 2: Find the median.

  • Since there are 8 numbers (even count), the median is the average of the 4th and 5th numbers in the ordered set.
  • The 4th number is 18, and the 5th number is 20.

Step 3: Calculate the median.

Median=18+202=19\text{Median} = \frac{18 + 20}{2} = 19

Thus, the median is 19, corresponding to option c).

Would you like further clarification or details on this solution?

Here are five related questions:

  1. What is the mean of the data set?
  2. How do you find the mode of a data set?
  3. What is the range of this data set?
  4. How does the median change if an additional number is added to the set?
  5. What is the difference between the median and the mean?

Tip: The median is a measure of central tendency that is resistant to extreme values (outliers).

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Math Problem Analysis

Mathematical Concepts

Median
Data Sets
Measures of Central Tendency

Formulas

Median = (n/2)th value for sorted data when even count

Theorems

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Suitable Grade Level

Grades 6-8