AP Statistics FRQ Practice

Practice FRQ 1 of 19

1. Dr. Aris, an agricultural researcher, is investigating the yield of two different varieties of tomato plants, Variety X and Variety Y. The yield is measured in kilograms (kg) of fruit per plant. Dr. Aris selected a random sample of 60 plants of Variety X and a random sample of 60 plants of Variety Y grown under identical conditions. The yields for each sample are summarized in the boxplots shown in Figure 1.

Figure 1. Boxplots of tomato yield (kg of fruit per plant) for Variety X and Variety Y (each sample size n = 60).

A clean, black-and-white statistical graphic containing two HORIZONTAL boxplots aligned to the same numeric x-axis.

Axes (REQUIRED):
- Horizontal axis (x-axis): labeled exactly "Yield (kg)" centered below the axis. The x-axis runs from 0 to 12 inclusive. Tick marks and numeric labels appear at every 1 kg: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. The tick length is uniform.
- Vertical axis (y-axis): labeled exactly "Variety" along the left side. The y-axis contains two categorical tick positions only, evenly spaced: the lower category labeled exactly "Variety X" and the upper category labeled exactly "Variety Y". No other y-axis numbers are shown.
- Origin label: the x-axis tick label "0" appears at the far left end of the x-axis at the axis intersection with the y-axis baseline.
- Arrows: arrowheads appear on the positive end of the x-axis (pointing right) and on the positive end of the y-axis (pointing upward).
- No gridlines.

Boxplot styling (applies to both):
- All boxplot elements are solid black lines of medium thickness.
- Each boxplot consists of a rectangular box from the first quartile to the third quartile, a vertical median line inside the box, and horizontal whiskers extending left and right from the box to the minimum and maximum non-outlier values.
- Outliers, when present, are marked as single asterisks placed directly on the yield scale at the correct x-value, aligned horizontally with the corresponding variety’s boxplot.

Variety X boxplot (lower row, aligned with the y-axis label "Variety X"):
- Left whisker endpoint is exactly at yield 2.0.
- Left edge of the box (first quartile, Q1) is exactly at yield 4.0.
- Median is a vertical line inside the box exactly at yield 5.0.
- Right edge of the box (third quartile, Q3) is exactly at yield 6.0.
- Right whisker endpoint (largest NON-outlier) is exactly at yield 6.0 so the whisker coincides with the right edge of the box (no visible whisker length beyond the box on the right).
- A single outlier is shown as an asterisk at yield 10.0, horizontally aligned with the Variety X boxplot and clearly separated to the right of the box.

Variety Y boxplot (upper row, aligned with the y-axis label "Variety Y"):
- Left whisker endpoint is exactly at yield 5.0.
- Left edge of the box (Q1) is exactly at yield 6.0.
- Median is a vertical line inside the box exactly at yield 8.0.
- Right edge of the box (Q3) is exactly at yield 9.0.
- Right whisker endpoint is exactly at yield 11.0.
- No outlier symbols appear anywhere on the Variety Y row.

Critical numerical constraints (must be visually exact):
- Variety X five-number summary shown by the box-and-whisker (excluding outlier symbol): minimum 2.0, Q1 4.0, median 5.0, Q3 6.0, maximum non-outlier 6.0; and a separate outlier point at 10.0.
- Variety Y five-number summary: minimum 5.0, Q1 6.0, median 8.0, Q3 9.0, maximum 11.0.

Curve/shape requirements note:
- This figure contains no curves; each boxplot is composed only of straight line segments (box edges, median line, and whiskers).

A. Compare the distributions of tomato yield for the sample of Variety X plants and the sample of Variety Y plants.

B. For the distribution of yield for the sample of Variety X plants, would you expect the mean to be greater than 5.0 kg, less than 5.0 kg, or equal to 5.0 kg? Justify your answer.

C. Dr. Aris creates a new dataset by combining the yields from the 60 Variety X plants and the 60 Variety Y plants.

i. What is the range of the combined data set? Show your work.

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

Practice FRQ 1 of 19

Figure 1. Boxplots of tomato yield (kg of fruit per plant) for Variety X and Variety Y (each sample size n = 60).

A. Compare the distributions of tomato yield for the sample of Variety X plants and the sample of Variety Y plants.

B. For the distribution of yield for the sample of Variety X plants, would you expect the mean to be greater than 5.0 kg, less than 5.0 kg, or equal to 5.0 kg? Justify your answer.

C. Dr. Aris creates a new dataset by combining the yields from the 60 Variety X plants and the 60 Variety Y plants.

i. What is the range of the combined data set? Show your work.

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