Question 1

The median is equal to the mean.

In this data set, the calculated mean and median both yield the same value, confirming that the median is equal to the mean. This equality arises from the specific distribution of the numbers in the data set.

A) The median is greater than the mean.

This statement is incorrect because the mean and median are equal in this data set. The calculation of both the mean and median shows that they result in the same numerical value, which means the median cannot be greater than the mean.

B) The range is less than the median.

This statement is also incorrect. The range of the data set, which is the difference between the maximum and minimum values (15 - 5 = 10), is greater than the median (10). Therefore, this option does not hold true.

C) The median is equal to the mean.

This statement is correct. For the given data set, the mean is calculated as (5 + 8 + 10 + 12 + 15) / 5 = 10, and the median, which is the middle value in the ordered set, is also 10. Thus, both measures are equal.

D) The mean is greater than the median.

This statement is incorrect as the mean and median are equal in this data set. Since both values are the same, it cannot be said that the mean is greater.

Conclusion

The correct answer is that the median is equal to the mean, as verified by the calculations for the provided data set. Options A, B, and D fail because they misinterpret the relationship between the mean and median or incorrectly assess the range. This clearly illustrates the importance of understanding these fundamental statistical concepts.