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 (below) 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 range formula

The range of a data - set is given by $Range = \text{Max}-\text{Min}$.

Step2: Read values from box - and - whisker plot

From the box - and - whisker plot, the minimum value (left - most point) is 10 and the maximum value (right - most point) is 50.

Step3: Calculate the range

$Range=50 - 10=40$.

Step4: Analyze part (b)

In a box - and - whisker plot, the median divides the data into two equal halves. If 28 is the median (the line inside the box), then the same number of data points are below 28 as are above 28.

Step5: Analyze part (c)

In a box - and - whisker plot, the upper 25% of the data lies between the third - quartile ($Q_3$) and the maximum value. If the third - quartile is 38 and the maximum is 50, the interval that gives the highest 25% of the data is 38 to 50.

Answer:

(a) 40
(b) The same number of rides had a distance under 28 as had a distance over 28.
(c) 38 to 50