What is the median of 28, 44, 20, 20
The Correct Answer and Explanation is:
Correct Answer:
The median of the numbers 28, 44, 20, 20 is 24.
Step-by-Step Explanation (With 300 Words):
To find the median of a set of numbers, we follow a specific process. The median is the middle value in a list when the numbers are arranged in ascending (or descending) order. If there is an even number of elements, the median is the average of the two middle numbers.
Let’s go through the process with the numbers:
Given numbers: 28, 44, 20, 20
Step 1: Sort the numbers in ascending order.
We arrange the numbers from smallest to largest:
20, 20, 28, 44
Step 2: Determine the number of elements.
There are 4 numbers, which is an even number.
Step 3: Find the two middle numbers.
In a list of 4 numbers, the two middle positions are the 2nd and 3rd numbers.
From our sorted list:
- 2nd number = 20
- 3rd number = 28
Step 4: Find the average of the two middle numbers. Median=20+282=482=24\text{Median} = \frac{20 + 28}{2} = \frac{48}{2} = 24
So, the median is 24.
Why Median Matters:
The median is a measure of central tendency, just like the mean (average) or mode. However, the median is less affected by extreme values (outliers), making it a more robust measure in many real-world applications. In this case, even though 44 is relatively large compared to the other numbers, it doesn’t distort the median. That’s why the median is often used in reporting income, housing prices, and other data where extremes could mislead.
In conclusion, by sorting the values and taking the average of the two central ones (since there’s an even count), we determined the median of 28, 44, 20, 20 is 24.
