Question

interpreting a box - and - whisker plot: problem type
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 eric sold in a day? (that is, what is the range of the data?)
(b) which of these best describes the numbers of plants eric sold this past spring?
the number of plants sold was below 56 on more days than it was above 56.
the number of plants sold was above 56 on more days than it was below 56.
the number of plants sold was below 56 for the same number of days that it was above 56.
(c) which of the following intervals gives the lowest 25% of the data?
40 to 51 51 to 52 51 to 53 52 to 53

Explanation:

Step1: Find the range

In a box - and - whisker plot, the range is calculated as \( \text{Range}=\text{Maximum value}-\text{Minimum value} \). From the plot, the minimum value is \( 40 \) and the maximum value is \( 62 \). So, \( 62 - 40=22 \).

Step2: Analyze the median

The median (vertical line inside the box) of the box - and - whisker plot divides the data into two equal parts. If the median is \( 56 \), then 50% of the data is below \( 56 \) and 50% is above \( 56 \).

Step3: Identify the first quartile (for lowest 25% of data)

The first quartile (\( Q_1 \)) represents the value below which 25% of the data lies. From the box - and - whisker plot, the first quartile is \( 51 \) and the minimum value is \( 40 \). But if we consider the box - and - whisker plot structure (assuming the first 'whisker' and first part of the box), the lowest 25% of the data is from the minimum value (if we assume the plot's left - most point as \( 40 \) is an outlier or not, but if we consider the box - start at \( 51 \)), the lowest 25% of the data (first quartile range) is from \( 51 \) (first quartile) to the median of the lower half. But if we assume the plot's left - most non - outlier (assuming the left - most 'whisker' end is \( 51 \)), the lowest 25% of the data is from \( 51 \) to \( 53 \) (assuming the box - and - whisker plot's first quartile at \( 51 \) and the median of the lower half (second quartile of the lower half) at \( 53 \)).

Answer:

(a) \( 22 \)
(b) The number of plants sold was below \( 56 \) for the same number of days that it was above \( 56 \).
(c) \( 51 \) to \( 53 \)