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

Two boxplots represent the heights of plants under Treatment A and Treatment B.

Treatment A: $Q_1 = 15$, median $= 20$, $Q_3 = 25$. Treatment B: $Q_1 = 18$, median $= 22$, $Q_3 = 24$.

Determine which treatment shows less variability. Justify your answer.

For a set of daily sales, the summary statistics are $\min = 50$, $Q_1 = 75$, $\text{median} = 100$, and $Q_3 = 150$. The maximum value in the dataset is recorded as $350$.

Use the $1.5 \times \text{IQR}$ rule to determine if the value of $350$ is an outlier.

A boxplot shows the first quartile at $15$, the median at $30$, and the third quartile at $45$.

State the median value of the dataset.

For a dataset with the following five-number summary: $\min = 3$, $Q_1 = 9$, $\text{median} = 12$, $Q_3 = 18$, and $\max = 35$, determine whether the value $35$ is an outlier using the $1.5 \times IQR$ rule.

Given the five-number summary: $\text{min} = 4, Q_1 = 8, \text{median} = 12, Q_3 = 16, \text{max} = 28$, describe the skewness of the data distribution.

A dataset of 200 values has five-number summary: $\min=2, Q_1=5, \text{median}=7, Q_3=10, \max=20$. Approximately how many values are below the median?

In a boxplot, $Q_1 = 10$, $\text{median} = 12$, and $Q_3 = 14$. Determine the percentage of the data that lies between $Q_1$ and $Q_3$.

The five-number summary of a dataset is: minimum $= 10$, $Q_1 = 20$, median $= 35$, $Q_3 = 50$, maximum $= 70$.

Calculate the interquartile range. [2 marks]

A dataset has a five-number summary: minimum = $12$, $Q_1 = 25$, median = $40$, $Q_3 = 55$, maximum = $80$. Determine the range of the dataset.

A boxplot of exam scores shows the median is closer to $Q_1$ than to $Q_3$, and the upper whisker is longer than the lower whisker. Is the distribution skewed left or right? Explain.

Dataset A has the five-number summary: $\text{min} = 5$, $Q_1 = 15$, $\text{median} = 25$, $Q_3 = 35$, $\text{max} = 45$. Dataset B has the five-number summary: $\text{min} = 0$, $Q_1 = 10$, $\text{median} = 20$, $Q_3 = 40$, $\text{max} = 50$.

Determine which dataset has greater variability. Justify your answer using 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.