The median of the following data is :
25, 34, 31, 23, 22, 26, 35, 29, 18, 32

Question

Accepted Answer

To determine the median of the given data set, we must first arrange the numbers in ascending order. The data set provided is:

25, 34, 31, 23, 22, 26, 35, 29, 18, 32

Arranging these numbers in ascending order gives us:

18, 22, 23, 25, 26, 29, 31, 32, 34, 35

The median is the middle value of a data set when it is ordered. Since there are 10 numbers in this data set (an even number), the median will be the average of the 5th and 6th numbers.

In the ordered list, the 5th number is 26 and the 6th number is 29. To find the median, we calculate the average of these two numbers:

Median = (26 + 29) / 2 = 55 / 2 = 27.5

Therefore, the median of the data set is 27.5, which corresponds to Option 3.

Explanation of why the other options are incorrect:

1. **Option 1 (26):** This option is incorrect because 26 is only one of the two middle numbers in the ordered data set. The median is the average of the two middle numbers, not just one of them.

2. **Option 2 (27):** This option is incorrect because the average of the two middle numbers (26 and 29) is 27.5, not 27. The calculation clearly shows that 27 is not the correct median.

3. **Option 4 (28.5):** This option is incorrect because the average of the two middle numbers (26 and 29) is 27.5, not 28.5. The calculation confirms that 28.5 is not the median.

In conclusion, the correct median of the data set is 27.5, which is why Option 3 is the correct answer.