AP Statistics FRQ Practice

📊AP Statistics

Guided Practice

Practice FRQ 1 of 191/19

1. Dr (see Figure 1). Aris, a materials engineer at a construction firm, is investigating the breaking strength of ceramic tiles made from two different clay mixtures, Mixture A and Mixture B.

Figure 1. Boxplots of breaking strength (MPa) for ceramic tiles made from Mixture A and Mixture B (n = 120 each).

A clean, black-and-white statistical graphic consisting of TWO HORIZONTAL boxplots aligned to the SAME horizontal number line.

Axes and layout (REQUIRED):
- Horizontal axis (x-axis): labeled exactly "Breaking strength (MPa)".
- X-axis numeric range: from 10 to 90.
- X-axis tick marks and labels: a tick and label at every 10 MPa: 10, 20, 30, 40, 50, 60, 70, 80, 90.
- The x-axis baseline is a straight horizontal line with an arrow at the positive (right) end.
- Vertical axis (y-axis): labeled exactly "Mixture".
- Y-axis has TWO category positions only, evenly spaced vertically: the TOP category labeled "Mixture A" and the BOTTOM category labeled "Mixture B".
- A vertical y-axis line is drawn at the left edge of the plotting area with an arrow at the positive (upward) end.
- Origin labeling requirement: place the text "0" at the intersection of the axes (bottom-left corner). (Note: the plotted x-scale begins at 10 MPa; the "0" is only an origin label at the axes intersection and is not a tick on the breaking-strength scale.)
- No title inside the plotting area. No grid lines.

Styling rules for BOTH boxplots:
- Each boxplot is drawn as a standard five-number-summary box-and-whisker plot.
- The box is a thin, unfilled rectangle (white interior) with a solid black outline.
- The median is a solid black vertical line inside the box.
- Whiskers are thin horizontal line segments extending from each end of the box to the minimum and maximum values.
- At each whisker endpoint (minimum and maximum), draw a short vertical cap line.
- Do NOT plot any outlier symbols (assume the whiskers reach the minimum and maximum values exactly as stated).

Top boxplot (Mixture A), positioned on the "Mixture A" row:
- Left whisker endpoint (minimum) is exactly at 20 MPa.
- Left edge of the box (first quartile, Q1) is exactly at 30 MPa.
- Median line inside the box is exactly at 35 MPa (explicitly aligned with the x-axis tick labeled 35 is NOT present; therefore the median line must be positioned halfway between the 30 and 40 ticks).
- Right edge of the box (third quartile, Q3) is exactly at 45 MPa (positioned halfway between the 40 and 50 ticks).
- Right whisker endpoint (maximum) is exactly at 70 MPa.
- Visual proportion must reflect exact distances on the shared scale: the right whisker segment (from 45 to 70) is 25 MPa long, and the left whisker segment (from 30 to 20) is 10 MPa long; therefore the right whisker is exactly 2.5 times the length of the left whisker.

Bottom boxplot (Mixture B), positioned on the "Mixture B" row:
- Left whisker endpoint (minimum) is exactly at 35 MPa (halfway between the 30 and 40 ticks).
- Left edge of the box (Q1) is exactly at 45 MPa (halfway between 40 and 50).
- Median line is exactly at 55 MPa (halfway between 50 and 60).
- Right edge of the box (Q3) is exactly at 65 MPa (halfway between 60 and 70).
- Right whisker endpoint (maximum) is exactly at 80 MPa.
- Visual proportion must reflect exact distances: the left whisker segment (from 45 down to 35) is 10 MPa, and the right whisker segment (from 65 up to 80) is 15 MPa, so the right whisker is exactly 1.5 times the left whisker.

Comparability constraints:
- Both boxplots share the same x-axis and must be horizontally aligned so that identical MPa values line up vertically.
- The widths of the boxes must match their IQRs exactly on the shared scale: Mixture A box spans 30 to 45 (15 MPa) and Mixture B box spans 45 to 65 (20 MPa).
- Ensure the value 35 MPa is visually interpretable: it must be clear that Mixture A’s median line lies exactly midway between the 30 and 40 tick marks, and Mixture B’s minimum lies at the same location (35 MPa).

A. Compare the distributions of breaking strength for the sample of tiles made from Mixture A and the sample of tiles made from Mixture B.

B. For the distribution of breaking strength for the sample of tiles made from Mixture A, would you expect the mean to be greater than 35 MPa, less than 35 MPa, or equal to 35 MPa? Justify your answer.

C. Dr. Aris creates a new dataset by combining the breaking strengths from the 120 tiles of Mixture A and the 120 tiles of Mixture B.

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 quartiles shown in the boxplots.