Question

the displayed figure is a histogram of the percent of on - time high school graduates in each state. which of the following could be the possible lower quartile value? a. 81%. b. 75%. c. 77%. d. 68% to 72%.

Explanation:

Step1: Recall lower - quartile concept

The lower quartile ($Q_1$) represents the 25th percentile of the data. In a histogram, we need to consider the cumulative frequency.

Step2: Analyze the histogram

Looking at the histogram, we know that the lower quartile value should be such that 25% of the data lies below it. Since the data is grouped in intervals, we can estimate. The first few intervals have relatively low frequencies. The interval starting from 66 - 69 has some data, but not enough to reach 25% of the total number of states. The interval 69 - 72 starts to accumulate more data. By visual inspection and considering the cumulative nature of quartiles, we can see that the value is likely in the 66 - 69 or 69 - 72 range. Among the given options, 68% to 72% is the most appropriate range for the lower - quartile value.

Answer:

d. 68% to 72%