Which of the following is the median of the data set below? 12, 19, 7, 14, 22, 26, 15

Rationale

The median of the data set is 15.

To find the median, the data set must first be arranged in ascending order. Once sorted, the median can be determined as the middle value in the ordered list, or the average of the two middle values if the number of observations is even. In this case, the sorted data set is 7, 12, 14, 15, 19, 22, 26, with 15 positioned centrally.

A (14) YOUR ANSWER

The value 14 is not the median because, in the sorted list, it is the third number rather than the middle number. The median requires the middle value, which in this ordered data set is 15, not 14.

B (15) CORRECT

This is the correct choice as it is the fourth number in the ordered list of seven values (7, 12, 14, 15, 19, 22, 26). Since there are seven values (an odd count), the median is simply the middle value, which is 15.

C (16) YOUR ANSWER

The number 16 does not appear in the data set at all. The median must be one of the values from the data set, and since 16 is absent, it cannot be the median.

D (19) YOUR ANSWER

While 19 is a number in the sorted list, it does not represent the median. It is located after the middle value; hence, it is too high to be the median of the data set.

Conclusion

The median is the middle value of a sorted data set, and in this case, it is 15. By arranging the numbers in order, we confirm that 15 is the median, as it sits in the center of the seven values. Choices A, C, and D all fail to represent the median correctly, illustrating the importance of proper ordering in determining this central tendency measure.

Which of the following is the median of the data set below? 12, 19, 7, 14, 22, 26, 15

The median of the data set is 15.

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