Question

the line plot shows the amount of time jason spent practicing basketball each day for 12 days. each x represents 1 day.
jason’s basketball practice
(line plot with xs over time in hours: 0, 1/4, 1/2, 3/4, 1, 1 1/4, 1 1/2, 1 3/4, 2)
what is the difference between the greatest and the least amount of time jason spent practicing basketball?
a. 3/4 hour
b. 1 hour
c. 1 1/4 hours
d. 1 1/2 hours

Explanation:

Step1: Identify greatest and least time

From the line plot, the least time is $\frac{1}{2}$ hour (where the first X's are) and the greatest time is $2$ hours (where the last X's are). Wait, no, wait. Wait, the x - axis labels: let's check again. Wait, the first X's are at $\frac{1}{2}$? Wait no, the x - axis marks: 0, $\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$, 1, $1\frac{1}{4}$, $1\frac{1}{2}$, $1\frac{3}{4}$, 2. Wait, the left - most X's are at $\frac{1}{2}$? Wait no, looking at the plot: the first X's (the left - most) are at $\frac{1}{2}$? Wait, no, the first X's are at $\frac{1}{2}$? Wait, no, let's count the positions. Wait, the least time: the left - most X is at $\frac{1}{2}$? Wait, no, the x - axis: 0, $\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$, 1, $1\frac{1}{4}$, $1\frac{1}{2}$, $1\frac{3}{4}$, 2. Wait, the first X's (the ones with two X's) are at $\frac{1}{2}$? Wait, no, maybe I misread. Wait, the greatest time is at 2 hours (the right - most X's) and the least time is at $\frac{1}{2}$? Wait, no, wait the left - most X's are at $\frac{1}{2}$? Wait, no, let's check the x - axis labels again. The x - axis has marks at 0, $\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$, 1, $1\frac{1}{4}$, $1\frac{1}{2}$, $1\frac{3}{4}$, 2. The left - most X's are at $\frac{1}{2}$ (two X's), then next at 1 (three X's), then $1\frac{1}{4}$ (one X), $1\frac{1}{2}$ (two X's), $1\frac{3}{4}$ (one X), 2 (three X's). Wait, no, maybe the least time is $\frac{1}{2}$ and the greatest is 2? Wait, no, that can't be. Wait, no, maybe I made a mistake. Wait, the problem says "the amount of time Jason spent practicing basketball each day". The line plot: the left - most X is at $\frac{1}{2}$? Wait, no, the first mark after 0 is $\frac{1}{4}$, then $\frac{1}{2}$. So the least time is $\frac{1}{2}$ hour? Wait, no, wait the X's: the left - most X's are at $\frac{1}{2}$ (two X's), then 1 (three X's), $1\frac{1}{4}$ (one X), $1\frac{1}{2}$ (two X's), $1\frac{3}{4}$ (one X), 2 (three X's). Wait, no, maybe the least time is $\frac{1}{2}$ and the greatest is 2? Wait, no, that would be a difference of $2-\frac{1}{2}=\frac{3}{2}=1\frac{1}{2}$, but that's option D. But wait, maybe I misread the least time. Wait, maybe the least time is $\frac{1}{2}$? No, wait, maybe the left - most X is at $\frac{1}{2}$? Wait, no, let's look again. The x - axis: 0, $\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$, 1, $1\frac{1}{4}$, $1\frac{1}{2}$, $1\frac{3}{4}$, 2. The X's: at $\frac{1}{2}$: two X's; at 1: three X's; at $1\frac{1}{4}$: one X; at $1\frac{1}{2}$: two X's; at $1\frac{3}{4}$: one X; at 2: three X's. Wait, so the least time is $\frac{1}{2}$ and the greatest is 2? Then the difference is $2-\frac{1}{2}=\frac{4 - 1}{2}=\frac{3}{2}=1\frac{1}{2}$? But that's option D. Wait, but maybe I made a mistake. Wait, no, maybe the least time is $\frac{1}{2}$? Wait, no, maybe the left - most X is at $\frac{1}{2}$, and the right - most at 2. So $2-\frac{1}{2}=1\frac{1}{2}$. But let's check the options. Option D is $1\frac{1}{2}$ hours. Wait, but let's re - examine. Wait, maybe the least time is $\frac{1}{2}$ and the greatest is 2? Wait, no, maybe the least time is $\frac{1}{2}$? Wait, no, maybe the x - axis is marked as 0, $\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$, 1, $1\frac{1}{4}$, $1\frac{1}{2}$, $1\frac{3}{4}$, 2. So the left - most X is at $\frac{1}{2}$, right - most at 2. So difference is $2-\frac{1}{2}=\frac{3}{2}=1\frac{1}{2}$. So the answer is D.

Step2: Calculate the difference

The greatest time is $2$ hours (from the line plot, the right - most X's are at 2) and the least time is $\frac{1}{2}$ hours (the left - most X's are at $\frac{1}{2}$). The difference is $2-\frac{1}{2}=\frac{4 - 1}{2}=\frac{3}{2}=1\frac{1}{2}$ hours.

Answer:

D. $1\frac{1}{2}$ hours