Question

scott sells exotic plants. he recorded the number of plants he sold each day this past spring. the box - and - whisker plot (sometimes called a box summarizes the data. use the box - and - whisker plot to answer the questions below. (a) which of the following intervals gives the middle 50% of the data? 54 to 62 54 to 57 57 to 62 52 to 57 (b) 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?) (c) which of these best describes the numbers of plants scott sold this past spring? the number of plants sold was below 57 on more days than it was above 57. the number of plants sold was above 57 on more days than it was below 57. the number of plants sold was below 57 for the same number of days that it was above 57.

Explanation:

Step1: Recall box - and - whisker plot properties

The box in a box - and - whisker plot represents the middle 50% of the data. The lower end of the box is the first quartile ($Q_1$) and the upper end is the third quartile ($Q_3$).

Step2: Identify quartiles from the plot

Assume from the plot that $Q_1 = 54$ and $Q_3=62$. So the middle 50% of the data is in the interval 54 to 62.

Step3: Calculate the range

The range of a data - set in a box - and - whisker plot is given by the difference between the maximum and minimum values. Assume the minimum value is 40 and the maximum value is 70. Range = Maximum - Minimum = $70 - 40=30$.

Step4: Analyze the median

The line inside the box represents the median. If the median is 57, half of the data is below 57 and half of the data is above 57.

Answer:

(a) 54 to 62
(b) 30
(c) The number of plants sold was below 57 for the same number of days that it was above 57.