Question

Sleepless nights Researchers recorded data on the amount of sleep reported each night during a week by a random sample of $20$high school students. Here are parallel boxplots comparing the distribution of time slept on all $7$nights of the study:

Use the graph to help answer the following questions.

a. Which distributions have a clear left-skewed shape?

b. Which outlier stands out the most, and why?

c. How does the typical amount of sleep that the students got compare on these seven nights?

d. On which night was there the most variation in how long the students slept? Justify your answer.

Short answer

a. The days are Monday, Wednesday and Sunday.

b. Outlier of Friday distribution.

c. Highest typical amount of sleep occurs on Friday and lowest amount of sleep occurs on Thursday.

d. Saturday night

Step-by-step solution

Given Information

It is given that:

On which day, distribution has a clear left skewed shape.

Distribution has skewed to left shape. If box of the plot lies close to top between whiskers of the plot and if horizontal line in box of box plot lies near top of box.

Hence distribution of Monday, Wednesday and Saturday has left skewed shape as box of the plot is lying near top between whiskers of box plot.

Outliers stands out the most

Outliers are represented by little circles. i.e. Tuesday, Thursday, Friday and Sunday.

Outliers of Friday stands out the most as it is far from box plot.

Typical Sleep students got

It is shown by horizontal lines in box of box plot and highest amount of sleep occurs where lowest typical amount of sleep occurs on Thursday and typical amount of sleep occurs decrease from Friday to Thursday.

Night with most variation in students sleep

Variation is showed by width between whiskers of box plot.

Width between whiskers of box plot is higher for Saturday. Hence, most variation on Saturday night.