Question Type 4: Interpretating information from box and whisker plots Exercises

In a boxplot, $Q1 = 10$, median = $12$, and $Q3 = 14$. What percentage of the data lies between $Q1$ and $Q3$?

A boxplot shows the first quartile at $15$, the median at $30$, and the third quartile at $45$. What is the median value of the dataset?

A dataset has five-number summary: minimum = $12$, $Q1 = 25$, median = $40$, $Q3 = 55$, maximum = $80$. Determine the range of the dataset.

A dataset of 200 values has five-number summary: $\text{min}=2$, $Q1=5$, $\text{median}=7$, $Q3=10$, $\text{max}=20$. Approximately how many values are below the median?

The five-number summary of a dataset is: minimum = $10$, $Q1 = 20$, median = $35$, $Q3 = 50$, maximum = $70$. Calculate the interquartile range.

A box and whisker plot has whiskers at $8$ and $62$, and the box spans from $20$ to $50$. Calculate the lengths of the lower and upper whiskers.

Given the five-number summary: $\text{min}=4$, $Q1=8$, $\text{median}=12$, $Q3=16$, $\text{max}=28$, describe the skewness of the data distribution.

A boxplot of exam scores shows the median is closer to $Q1$ than to $Q3$, and the upper whisker is longer than the lower whisker. Is the distribution skewed left or right? Explain.

Two boxplots represent heights of plants under Treatments A and B. Treatment A: $Q1=15$, median = $20$, $Q3=25$. Treatment B: $Q1=18$, median = $22$, $Q3=24$. Which treatment shows less variability?

Dataset A has five-number summary: $\text{min}=5$, $Q1=15$, $\text{median}=25$, $Q3=35$, $\text{max}=45$. Dataset B has $\text{min}=0$, $Q1=10$, $\text{median}=20$, $Q3=40$, $\text{max}=50$. Which dataset has greater variability? Justify using interquartile range.

A boxplot for daily sales shows $\text{min}=50$, $Q1=75$, median = $100$, $Q3=150$, $\text{max}=300$. A data point at $350$ lies beyond the upper whisker. Use the $1.5\times IQR$ rule to determine if $350$ is an outlier.

For a dataset with five-number summary: $\text{min}=3$, $Q1=9$, $\text{median}=12$, $Q3=18$, $\text{max}=30$, determine whether the value $35$ is an outlier using the $1.5\times IQR$ rule.