Question

per hour quits and is replaced with a person earning 30 per hour. the graph of
plot 1

plot 2
how does the mean and median change from plot 1 to plot 2?
the mean and median remain the same.
the mean decreases, and the median remains the same.
the mean remains the same, and the median decreases.
the mean and median decrease.

Explanation:

Step1: Analyze Median

The median is the middle value of a dataset (or the average of the two middle values for even - sized datasets). In a box - plot, the line inside the box represents the median. Looking at Plot 1 and Plot 2, the position of the median line (inside the box) does not change. So the median remains the same.

Step2: Analyze Mean

The mean is calculated as the sum of all data points divided by the number of data points. In Plot 1, there is a long tail on the right (extending to 15), which means there are some relatively large data values. In Plot 2, the right - hand tail is shorter (does not extend as far). This implies that we are replacing a relatively large data value (from the long tail in Plot 1) with a smaller data value (since the tail is shorter in Plot 2). When we replace a large value with a smaller value, the sum of the data points will decrease, while the number of data points remains the same. Since the mean is $\frac{\text{Sum of data points}}{\text{Number of data points}}$, a decrease in the sum (with the number of data points constant) will lead to a decrease in the mean.

Answer:

The mean decreases, and the median remains the same.