Question

What is the median of the following data set? $$7,17,53,23,4,2,4$$ (A) 4 (B) 7 (C) 15.7 (D) 23

Short answer

The median is 7.

Step-by-step solution

- Sort the Data Set

First, arrange the numbers in ascending order: 2, 4, 4, 7, 17, 23, 53.

- Identify the Number of Data Points

Count the numbers in the data set. There are 7 numbers.

- Locate the Median

Since there are 7 data points (an odd number), the median is the middle number. The middle number is the 4th value in the ordered list.

- Find the Median

The middle number (4th value) in the ordered list is 7.

Key concepts

sorting data

To find the median of a data set, the first step is to arrange the numbers in ascending order. This means to sort the data from the smallest value to the largest. Sorting helps organize the data and makes it easier to find the median. For example, let's look at the original data set: [7, 17, 53, 23, 4, 2, 4].
After sorting, the values are: [2, 4, 4, 7, 17, 23, 53]. Notice how we start from the lowest number (2) and end with the highest number (53).
Sorting is the foundation for many statistical calculations, so it's vital to understand this step thoroughly.

identifying the median

Once the data set is sorted, the next step is to identify the median. The median is the middle number in an ordered list of numbers. If the number of data points is odd, the median is simply the value at the middle position.
In our sorted data set [2, 4, 4, 7, 17, 23, 53], we have 7 data points. Since 7 is an odd number, the median is the 4th value in the list, which is 7. Finding the median when the number of data points is even is a bit different, but since we are working with an odd number here, the process is straightforward: just pick the middle number in the sorted list.

counting data points

To identify the median accurately, you need to count the total number of data points in your set. Counting the data points helps determine the position of the median. Let's refer back to our dataset [2, 4, 4, 7, 17, 23, 53].
By counting each number, we see there are 7 data points. Knowing the total number of data points confirms whether the data set is odd or even, which is crucial because:

• If the number of data points is odd, the median is the middle value.
• If the number of data points is even, the median is the average of the two middle values.

In our example, with 7 being an odd number, we can assert that the median will be at the 4th position in the sorted list.