The histogram below displays the distribution of 50 ages at death due to trauma (unnatural accidents and homicides) that were observed in a certain hospital during a week. Which of the following are the appropriate numerical measures to describe the center and spread of the above distribution?

a. The mean and the median

b. The IQR and the standard deviation

c. The mean and the standard deviation

d. The median and the IQR

d. The median and the IQR

Step-by-step explanation:

The median separates the upper half from the lower half of a set. So 50% of the values in a data set lie at or below the median, and 50% lie at or above the median. This means that the median is the appropriate numerical measure to describe the center.

The first quartile (Q1) separates the lower 25% from the upper 75% of a set. So 25% of the values in a data set lie at or below the first quartile, and 75% of the values in a data set lie at or above the first quartile.

The third quartile (Q3) separates the lower 75% from the upper 25% of a set. So 75% of the values in a data set lie at or below the third quartile, and 25% of the values in a data set lie at or the third quartile.

The quartiles are used to measure the spread of a data-set.

The interquartile range (IQR), is Q3-Q1.

So the correct answer is:

d. The median and the IQR