Question

movie length (minutes)
in which range(s) does 75% of the data lie? check all of the boxes that apply.
81 minutes and 109 minutes
81 minutes and 126 minutes
95 minutes and 138 minutes
109 minutes and 126 minutes
what percent of the data lies between 109 minutes and 138 minutes?

Explanation:

Step1: Recall quartile properties

In a box - and - whisker plot, the first quartile ($Q_1$) represents the 25th percentile, the second quartile ($Q_2$ or median) represents the 50th percentile, and the third quartile ($Q_3$) represents the 75th percentile. The inter - quartile range (IQR) which is $Q_3 - Q_1$ contains 50% of the data. The range from the minimum value to $Q_3$ contains 75% of the data.

Step2: Analyze the box - and - whisker plot

Assume the minimum value is around 81 (the start of the left - most whisker), and $Q_3$ is around 126. So the range from 81 minutes to 126 minutes contains 75% of the data. Also, if we consider a wider range that includes the minimum and $Q_3$, a range like 95 minutes and 138 minutes which is wider and also contains 75% of the data.

Step3: Calculate percentage between 109 and 138

If we assume 109 is $Q_1$ and 138 is close to the maximum or at least beyond $Q_3$. The percentage of data between $Q_1$ and the maximum (or a value beyond $Q_3$) is more than 50%. Since $Q_1$ is the 25th percentile, the percentage of data between 109 and 138 is 75 - 25=50% (if 138 is the maximum) or more if 138 is beyond $Q_3$.

Answer:

• In which range(s) does 75% of the data lie?
• 81 minutes and 126 minutes
• 95 minutes and 138 minutes
• What percent of the data lies between 109 minutes and 138 minutes?
• 50% or more