The median of the following data : 25, 34, 31, 23, 22, 26, 35, 28, 20, 32

Question

Accepted Answer

To determine the median of the given data set, we first need to arrange the numbers in ascending order. The data set provided is: 25, 34, 31, 23, 22, 26, 35, 28, 20, 32.

Step 1: Arrange the data in ascending order:
20, 22, 23, 25, 26, 28, 31, 32, 34, 35

Step 2: Identify the median:
Since there are 10 numbers in the data set, which is an even number, the median will be the average of the 5th and 6th numbers in this ordered list.

The 5th number is 26, and the 6th number is 28.

Step 3: Calculate the median:
Median = (26 + 28) / 2 = 54 / 2 = 27

Therefore, the median of the data set is 27, which corresponds to Option 1.

Explanation for why each option is correct or incorrect:

1. **Option 1 (27)**: This is the correct answer because, as calculated, the median of the ordered data set is 27. The median is the middle value when the numbers are arranged in order, and for an even number of observations, it is the average of the two middle numbers.

2. **Option 2 (28)**: This option is incorrect because 28 is one of the middle numbers used to calculate the median, but it is not the median itself. The median is the average of 26 and 28, which is 27.

3. **Option 3 (26)**: This option is incorrect because 26 is the other middle number used to calculate the median, but it is not the median itself. The median is the average of 26 and 28, which is 27.

4. **Option 4 (25)**: This option is incorrect because 25 is not involved in the calculation of the median. It is simply one of the numbers in the data set and does not represent the middle value or the average of the middle values.

In conclusion, Option 1 is the correct answer because the median of the given data set is 27, as determined by the proper calculation method for an even number of observations.