AP Statistics FRQ Practice

📊AP Statistics

Practice FRQ 1 of 191/19

1. Ms (see Figure 1). Gentry, an agricultural scientist, is investigating the weights of grapefruits from two different varieties, Variety A and Variety B, grown in a specific region. She wants to determine if there are significant differences in the weight distributions to decide which variety is more suitable for commercial packaging.

Figure 1. Boxplots of Grapefruit Weights (ounces) for Variety A and Variety B

A clean, black-and-white statistical graphic showing two HORIZONTAL boxplots aligned to a shared horizontal number line.

Axes and layout (treat this as a graph with a categorical y-axis):
- X-axis (horizontal): labeled exactly "Weight (ounces)" centered below the axis.
- X-axis numeric range: starts at 6 on the far left and ends at 24 on the far right.
- X-axis tick marks: labeled at every 2 ounces with the visible tick labels: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.
- Y-axis (vertical): labeled exactly "Variety" along the left side.
- Y-axis category positions: two equally spaced category levels.
- The upper category label reads "Variety A".
- The lower category label reads "Variety B".
- Origin requirement: place the label "0" at the lower-left intersection of the axes, but keep the plotted x-range and tick labels as 6 through 24; the "0" is only an axis-origin label and is not used as a tick on the weight scale.
- Arrows: include arrowheads on the positive (right) end of the x-axis and on the positive (up) end of the y-axis.
- No gridlines.

Boxplot styling rules (apply to BOTH varieties):
- All lines are solid black with uniform medium thickness.
- Each boxplot has: a left whisker line, a rectangular box, a median line inside the box, and a right whisker line.
- Whisker endpoints are marked with short vertical endcaps (small vertical line segments) exactly at the minimum and maximum values.
- The median is drawn as a vertical line segment spanning the full height of the box.

Exact numerical five-number summaries (these must be placed exactly on the x-axis scale at the labeled tick values):

Variety A (upper boxplot, aligned horizontally with the "Variety A" y-category):
- Minimum (left whisker endcap) is exactly at 8 ounces.
- First quartile Q1 (left edge of the box) is exactly at 10 ounces.
- Median (vertical line inside the box) is exactly at 12 ounces; this median line must align precisely with the x-axis tick labeled 12.
- Third quartile Q3 (right edge of the box) is exactly at 15 ounces; place the right edge of the rectangle halfway between the ticks labeled 14 and 16.
- Maximum (right whisker endcap) is exactly at 19 ounces; place this endcap halfway between the ticks labeled 18 and 20.
- Whiskers: a horizontal line connects 8 to 10 on the left, and another horizontal line connects 15 to 19 on the right.

Variety B (lower boxplot, aligned horizontally with the "Variety B" y-category):
- Minimum (left whisker endcap) is exactly at 12 ounces; this must align precisely with the tick labeled 12.
- First quartile Q1 (left edge of the box) is exactly at 15 ounces; place the left edge of the rectangle halfway between the ticks labeled 14 and 16.
- Median (vertical line inside the box) is exactly at 17 ounces; place this median line halfway between the ticks labeled 16 and 18.
- Third quartile Q3 (right edge of the box) is exactly at 19 ounces; place this edge halfway between the ticks labeled 18 and 20.
- Maximum (right whisker endcap) is exactly at 22 ounces; this must align precisely with the tick labeled 22.
- Whiskers: a horizontal line connects 12 to 15 on the left, and another horizontal line connects 19 to 22 on the right.

Relative placement and separation:
- The two boxplots are horizontally aligned to the same x-axis and vertically separated so they do not overlap.
- The upper plot (Variety A) sits centered on the upper y-category line; the lower plot (Variety B) sits centered on the lower y-category line.
- No additional annotations, no data points, and no outlier symbols are shown.

Title handling:
- Do NOT place a title inside the plotting area. The only text inside/near the axes should be axis labels, category labels, and the numeric tick labels on the x-axis.

A. Compare the distributions of weight for the sample of Variety A grapefruits and the sample of Variety B grapefruits.

B. For the distribution of weight for the sample of Variety A grapefruits, would you expect the mean to be greater than 12 ounces, less than 12 ounces, or equal to 12 ounces? Justify your answer.

i. What is the range of the combined data set? Justify your answer.

ii. What is a possible value of the median of the combined data set? Justify your answer by referencing the boxplots shown.

📊AP Statistics

Practice FRQ 1 of 191/19

Figure 1. Boxplots of Grapefruit Weights (ounces) for Variety A and Variety B

A. Compare the distributions of weight for the sample of Variety A grapefruits and the sample of Variety B grapefruits.

B. For the distribution of weight for the sample of Variety A grapefruits, would you expect the mean to be greater than 12 ounces, less than 12 ounces, or equal to 12 ounces? Justify your answer.

i. What is the range of the combined data set? Justify your answer.

ii. What is a possible value of the median of the combined data set? Justify your answer by referencing the boxplots shown.