Question

a farmer weighed a sample of pumpkins from her crop. she recorded the weight (in kg) of each pumpkin. the box-and-whisker plot (sometimes called a boxplot) summarizes these weights.
use the box-and-whisker plot to answer the following.
(a) what is the median weight?
(b) what is the lightest weight?
(c) what is the first quartile (q₁) of the weights?

Explanation:

Part (a)

Step1: Recall boxplot median

In a box - and - whisker plot, the median is represented by the line inside the box. Looking at the plot, we identify the position of this line on the weight axis.
From the plot, the line inside the box (representing the median) is at 28 kg (assuming the markings: let's check the axis. The axis has marks at 10,15,20,25,30,35,40,45,50. The box is between 20 - 35? Wait, no, the plot's box: the left end of the first box is at 20? Wait, the whisker starts at 18? Wait, maybe I misread. Wait, the x - axis: let's count the ticks. From 10 to 15: 5 units, 15 to 20:5 units. The first whisker starts at 18? No, the leftmost whisker is at 18? Wait, no, the problem's plot: the left whisker is at 18? Wait, no, the user's plot: the x - axis is from 10 to 50, with marks at 10,15,20,25,30,35,40,45,50. The box is split into two parts, and the median line is at 28? Wait, maybe the correct median is 28? Wait, no, maybe the median is 28. Wait, actually, in a boxplot, the median is the middle line of the box. Let's assume that the box is from 20 to 36, and the median is at 28. So the median weight is 28 kg.

Step2: Confirm median position

The median in a box - and - whisker plot is the vertical line (or horizontal, depending on orientation) inside the box. By identifying this line on the weight scale (x - axis), we get the median value.

Step1: Recall boxplot minimum

In a box - and - whisker plot, the lightest weight (minimum value) is represented by the left - most end of the left whisker.
Looking at the plot, the left - most point of the left whisker is at 18 kg (assuming the x - axis: the left whisker starts at 18). So the lightest weight is the value at the end of the left whisker.

Step2: Identify minimum from plot

The left whisker extends to the minimum value of the data set. From the plot, the left - most point of the left whisker is at 18 kg.

Step1: Recall boxplot first quartile

In a box - and - whisker plot, the first quartile ($Q_1$) is the left - hand end of the box.
Looking at the plot, the left end of the box (the start of the box) is at 20 kg (assuming the box starts at 20). So $Q_1$ is the value at the left end of the box.

Step2: Identify $Q_1$ position

The first quartile ($Q_1$) in a box - and - whisker plot is the left boundary of the box. By finding this boundary on the weight axis, we get the value of $Q_1$.

Answer:

28 (assuming the plot's median line is at 28. If there was a different marking, but based on typical boxplot interpretation, the median is the line in the box. If the plot's median line is at 28, then the answer is 28)

Part (b)