Question

daren grows both squash and cucumbers in his garden. each week during the growing season, daren counts the total number of squash and cucumber he picked. then at the end of the season, these data sets are compiled into the following box plots: box plot: number of vegetables produced, squash and cucumbers, weekly output axis with 10,20,30,40,50,60 based on these box plots, choose all of the following statements that are true. show your work here the maximum weekly output for the squash plants is 10 larger than the maximum weekly output for the cucumber plants. the data for the squash plants has a higher interquartile range (iqr) than the data for the cucumber plants. the median weekly output for the cucumber plants is 10 larger than the median value for the squash plants. the range in the weekly output is larger for the cucumber plants than for the squash plants. the minimum weekly output that the squash plants produced is less than the minimum weekly output that the cucumber plants produced.

Explanation:

To solve this, we analyze each statement using box - plot components (minimum, Q1, median, Q3, maximum, IQR = Q3 - Q1, range = maximum - minimum).

Statement 1: Maximum weekly output

From the box - plot, the maximum for squash and cucumbers: Let's assume the maximum for squash is around 65 and for cucumbers around 65 (visually, the whiskers end at similar points). So, the maximum weekly output for squash is not 10 larger than that for cucumbers. This statement is false.

Statement 2: Interquartile Range (IQR)

The IQR is the length of the box (Q3 - Q1). The box for squash is longer than the box for cucumbers. So, the IQR of squash data is higher than that of cucumber data. This statement is true.

Statement 3: Median weekly output

The median is the line inside the box. The median for cucumbers (around 45) and for squash (around 35). The median of cucumbers is 10 larger than that of squash. This statement is true.

Statement 4: Range in weekly output

Range = maximum - minimum. The minimum for both seems similar, and the maximum also seems similar. The length of the whiskers (from min to max) for cucumbers and squash: visually, the range for cucumbers is not larger than that for squash. This statement is false.

Statement 5: Minimum weekly output

The minimum (start of the left whisker) for squash is around 15 and for cucumbers around 20. So, the minimum weekly output of squash is less than that of cucumbers. This statement is true.

Answer:

The true statements are:

• The data for the squash plants has a higher interquartile range (IQR) than the data for the cucumber plants.
• The median weekly output for the cucumber plants is 10 larger than the median value for the squash plants.
• The minimum weekly output that the squash plants produced is less than the minimum weekly output that the cucumber plants produced.