Question

use the box - and - whisker plot to answer the questions below. (a) what is the difference of the highest number and the lowest number of plants scott sold in a day? (that is, what is the range of the data?) (b) which of these best describes the numbers of plants scott sold this past spring? the number of plants sold was below 60 on more days than it was above 60. the number of plants sold was above 60 on more days than it was below 60. the number of plants sold was below 60 for the same number of days that it was above 60. (c) which of the following intervals gives the highest 25% of the data? 60 to 62 60 to 64 62 to 64 64 to 70

Explanation:

Step1: Recall range definition

The range of a data - set in a box - and - whisker plot is the difference between the maximum and minimum values.

Step2: Identify max and min from box - and - whisker plot

From the box - and - whisker plot, the maximum value is 70 and the minimum value is 40.

Step3: Calculate the range

Range = Maximum value - Minimum value = 70 - 40 = 30.

For part (b):
In a box - and - whisker plot, the median divides the data into two halves. The lower half of the data is below the median and the upper half is above the median. The first quartile ($Q_1$) divides the lower half of the data into two parts, and the third quartile ($Q_3$) divides the upper half of the data into two parts. 25% of the data is above $Q_3$ and 25% of the data is below $Q_1$.
If we want to find the interval that has the highest 25% of the data, we are looking at the values above the third - quartile ($Q_3$). In a box - and - whisker plot, the third - quartile value is around 64. So the interval 64 to 70 contains the highest 25% of the data.

Answer:

(a) 30
(b) 64 to 70