There are 20 men in a room whose heights are reflected in inches as 68, 70, 73, 67, 71, 68, 76, 70, 73, 66, 68, 69, 71, 74, 73, 72, 65, 60, 70, and 78 inches respectively. What is the median of these data?

Rationale

The median of the given data is 70 inches.

To find the median, the data must first be sorted in ascending order. The median is the middle value, which, for an even number of observations, is the average of the two middle values. In this case, after sorting the heights, the two middle values are 70 and 70, resulting in a median of 70 inches.

A (71) YOUR ANSWER

Choosing 71 as the median overlooks the correct positioning of the sorted data. After arranging the heights from shortest to tallest, the middle values are both 70, not 71. The median must accurately reflect the center of the dataset based on the ordered values.

B (68) YOUR ANSWER

The value 68 is simply one of the heights in the dataset and does not represent the median. The median requires calculating the average of the center values in a sorted list, which, in this case, is clearly depicted as 70, making 68 an incorrect option.

C (73) YOUR ANSWER

While 73 is also among the recorded heights, it does not serve as the median. After ordering the heights, it is clear that the two middle values are 70 and 70. Hence, 73 does not correspond to the central tendency of the data set.

D (70) CORRECT

This is the correct median value, as it represents the average of the two middle heights in the sorted list. In a dataset with an even number of observations, the median is calculated from the two middle values, which, in this case, are both 70.

Conclusion

The median is a statistical measure of central tendency that indicates the middle value of a sorted dataset. For the heights provided, the correct median, calculated from the two central values of the ordered list, is 70 inches. This value captures the essence of the data efficiently, while the other options fail to identify the accurate central tendency.

There are 20 men in a room whose heights are reflected in inches as 68, 70, 73, 67, 71, 68, 76, 70, 73, 66, 68, 69, 71, 74, 73, 72, 65, 60, 70, and 78 inches respectively. What is the median of these data?

The median of the given data is 70 inches.

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