Question

martina is training for a cycling race. she recorded the distance (in kilometers) of several of her training rides. the box - and - whisker plot (sometimes called a boxplot) summarizes the data.
use the box - and - whisker plot to answer the questions below.
(a) what is the difference of the longest distance and the shortest distance training ride? (that is, what is the range of the data?)
(b) which of these best describes the distances (in kilometers) of martinas training rides?
there were more rides with a distance under 28 than with a distance over 28.
there were more rides with a distance over 28 than with a distance under 28.
the same number of rides had a distance under 28 as had a distance over 28.
(c) which of the following intervals gives the highest 25% of the data?
28 to 33 28 to 38 33 to 38 38 to 50

Explanation:

Step1: Identify min and max from box - and - whisker plot

The minimum value of the data from the box - and - whisker plot is 15 km and the maximum value is 50 km.

Step2: Calculate the range

Range = Maximum - Minimum = $50 - 15=35$ km.

Step3: Analyze the median position for part (b)

The median of a box - and - whisker plot divides the data into two equal halves. If we assume the median is at 28 (approximate visual inspection), the number of data points below the median is the same as the number of data points above the median. So, the same number of rides had a distance under 28 as had a distance over 28.

Step4: Recall quartile concept for part (c)

The upper 25% of the data lies above the third - quartile ($Q_3$). In a box - and - whisker plot, the box represents the middle 50% of the data (from $Q_1$ to $Q_3$). The upper 25% of the data is from $Q_3$ to the maximum value. If we assume $Q_3$ is around 38 (approximate visual inspection), the interval for the highest 25% of the data is 38 to 50.

Answer:

(a) 35
(b) The same number of rides had a distance under 28 as had a distance over 28.
(c) 38 to 50