The question asks us to find the median of the given set of data: 15, 30, 20, 10, 25, 35, 18, 21, 28.

Understanding the Median

The median is a measure of central tendency. It is the middle value in a data set that is arranged in ascending or descending order. If there is an odd number of data points, the median is the single middle value. If there is an even number of data points, the median is the average of the two middle values.

Steps to Calculate the Median

To find the median of a data set, follow these steps:

1. Arrange the data points in ascending order (from smallest to largest).
2. Count the total number of data points, let's call this 'n'.
3. Determine the median based on whether 'n' is odd or even:
   • If 'n' is an odd number, the median is the value at the \(\left(\frac{n+1}{2}\right)\)-th position in the ordered list.
   • If 'n' is an even number, the median is the average of the values at the \(\left(\frac{n}{2}\right)\)-th position and the \(\left(\frac{n}{2} + 1\right)\)-th position in the ordered list.

Calculating the Median for the Given Data

Let's apply these steps to the given data set: 15, 30, 20, 10, 25, 35, 18, 21, 28.

Step 1: Arrange the data in ascending order.

The data arranged in ascending order is:

10, 15, 18, 20, 21, 25, 28, 30, 35

Step 2: Count the number of data points (n).

There are 9 data points in the set.

So, n = 9.

Step 3: Determine the median.

Since 'n' is 9 (which is an odd number), the median is the value at the \(\left(\frac{n+1}{2}\right)\)-th position.

Position = \(\left(\frac{9+1}{2}\right)\) = \(\left(\frac{10}{2}\right)\) = 5th position.

Now, we find the value at the 5th position in our ordered data list (10, 15, 18, 20, 21, 25, 28, 30, 35).

The value at the 5th position is 21.

Therefore, the median of the data set is 21.

Result

The median of the data set 15, 30, 20, 10, 25, 35, 18, 21, 28 is 21.

This matches option 4.

Revision Table: Key Statistics Terms

Additional Information: Measures of Central Tendency

The median, mean, and mode are the three most common measures of central tendency. They each provide a single value that attempts to describe the center of a data set.

• The median is useful when the data set contains outliers, as it is not affected by extremely large or small values like the mean is.
• The mean is sensitive to every value in the data set and is often used for symmetrical distributions.
• The mode is most useful for categorical data or when you want to know the most typical value.

Choosing the appropriate measure of central tendency depends on the nature of the data and the goal of the analysis.