Find the median of the following data set: 1, 4, 2, 3, 9, 7, 12, 1, 4, 2, 8, 11, 3, 2, 4

Rationale

The median of the data set is 4.

To find the median, the data set must first be ordered from smallest to largest. After sorting the numbers—1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 7, 8, 9, 11, 12—the middle value emerges as 4, which is the fifth number in a set of fifteen values.

A (3.4) YOUR ANSWER

The value 3.4 does not represent the median of the sorted data set. Instead, it is a miscalculation that does not correspond to any of the actual values in the data set. The median should be a number from the data itself, while 3.4 lies between the numbers 3 and 4, thus not suitable as the median.

B (5.2) YOUR ANSWER

5.2 is also not a value present in the data set. The median is defined as the middle value of a sorted list, and since 5.2 does not appear in the ordered data, it cannot be the median. The actual middle value of the sorted set is 4, not 5.2.

C (11) YOUR ANSWER

While 11 is a value in the data set, it is not the median. The median is determined by the central position of the sorted list, which in this case is 4. The value 11 is much higher in the ordered set, specifically the twelfth number, therefore it cannot represent the median.

D (4) CORRECT

4 is the correct median as it is the middle number in the ordered data set of 15 values. With the numbers sorted, the fifth value is 4, confirming it as the median.

Conclusion

The median serves as a measure of central tendency, identifying the middle value of a data set when ordered. For the given data set, after sorting, the median is found to be 4, which serves as a crucial statistical measure. Incorrect options like 3.4, 5.2, and 11 do not represent the central value of the ordered data, reinforcing that the median accurately represents the data's center.

Find the median of the following data set: 1, 4, 2, 3, 9, 7, 12, 1, 4, 2, 8, 11, 3, 2, 4

The median of the data set is 4.

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