Fiveable
📊AP Statistics
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📊AP Statistics

FRQ 1 – Focus on Exploring Data
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Unit 1: Exploring One-Variable Data
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Guided Practice

Practice FRQ 1 of 191/19
1. Mr. Henderson, the manager of a large apple orchard, is investigating the weights of two different apple varieties, Crimson Crisp and Golden Delicious, to determine if they meet shipping standards. He wants to compare the distributions of weights for the two varieties.

Figure 1. Boxplots of Apple Weights (grams) for Crimson Crisp and Golden Delicious (each sample size n = 60).

A clean, black-and-white statistical graphic showing TWO HORIZONTAL boxplots stacked vertically and aligned to the SAME x-axis scale. Axes (REQUIRED): - X-axis (horizontal): labeled exactly "Weight (grams)" centered below the axis. The axis runs from 100 to 250. Tick marks and numeric tick labels are shown every 10 grams: 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250. The tick labels are directly under their ticks. - Y-axis (vertical): labeled exactly "Variety" along the left side. The vertical range runs from 0 to 2. Tick marks and numeric tick labels are shown every 1 unit: 0, 1, 2. - Origin: the point where x = 100 and y = 0 is labeled "0" at the intersection corner of the axes (bottom-left corner). - Arrows: arrows on the positive ends of both axes (right end of the x-axis and top end of the y-axis). Y-axis category placement (so the two boxplots do not drift vertically): - The TOP boxplot is centered exactly on the horizontal level y = 1.5 and is labeled "Crimson Crisp" on the left, aligned with that y level. - The BOTTOM boxplot is centered exactly on the horizontal level y = 0.5 and is labeled "Golden Delicious" on the left, aligned with that y level. Boxplot styling rules (apply to BOTH varieties): - All boxplot lines are solid black, medium thickness. - Each box is a rectangle with its left edge at the first quartile (Q1) and right edge at the third quartile (Q3). - The median is drawn as a single vertical line segment inside the box at the median value. - Whiskers extend horizontally from the box edges to the minimum and maximum NON-OUTLIER values. - Whisker endpoints are drawn with short vertical caps. - Outliers are shown as small open circles. - No gridlines. TOP boxplot: "Crimson Crisp" (centered at y = 1.5) - Minimum (left whisker endpoint) is exactly at 120 grams. - First quartile Q1 (left edge of the box) is exactly at 140 grams. - Median (vertical line inside the box) is exactly at 150 grams. - Third quartile Q3 (right edge of the box) is exactly at 160 grams. - Maximum (right whisker endpoint) is exactly at 180 grams. - There are NO outlier symbols for Crimson Crisp. - Visual spacing constraint to enforce symmetry appearance: the left whisker length (from 140 down to 120) is exactly the same horizontal length as the right whisker length (from 160 up to 180). BOTTOM boxplot: "Golden Delicious" (centered at y = 0.5) - Minimum (left whisker endpoint) is exactly at 130 grams. - First quartile Q1 (left edge of the box) is exactly at 160 grams. - Median (vertical line inside the box) is exactly at 175 grams. - Third quartile Q3 (right edge of the box) is exactly at 190 grams. - Right whisker endpoint (maximum NON-OUTLIER) is exactly at 210 grams (this must be a whisker cap, not a dot). - One outlier is plotted as a small open circle exactly at 230 grams, horizontally aligned with the Golden Delicious boxplot centerline (y = 0.5). - Separation constraint so the outlier is not mistaken for the whisker end: there is a visible gap between the right whisker cap at 210 and the outlier circle at 230. - Skewness constraint: the right whisker segment from 190 to 210 is visibly longer than the left whisker segment from 160 to 130. No curve shapes are present (this figure contains only boxplots), so there are no concavity/inflection/asymptote features to include. All visible text in the figure must be limited to: axis labels "Weight (grams)", "Variety"; y-category labels "Crimson Crisp" and "Golden Delicious"; x-axis tick labels from 100 to 250 by 10; y-axis tick labels 0, 1, 2; and the origin label "0" at the bottom-left axis intersection.
A. Compare the distributions of weight for the sample of Crimson Crisp apples and the sample of Golden Delicious apples shown in Figure 1.
B. For the distribution of weight for the sample of Golden Delicious apples, would you expect the mean to be greater than 175 grams, less than 175 grams, or equal to 175 grams? Justify your answer.
C.
i. Mr. Henderson combines the data from the 60 Crimson Crisp apples and the 60 Golden Delicious apples into a single dataset. What is the range of the combined data set? Show your work.
ii. What is a possible value for the median of the combined data set? Justify your answer by referencing the quartiles shown in the boxplots in Figure 1.
Pep