AP Statistics Graphs of Quantitative Data and Shape Worksheet Solutions (PDF)

(a) 6 students.

(b) \(2+1+1=4\).

(c) \(2+4=6\) students, and \(\frac{6}{20}=30\%\).

6; 4; 30%.

The value 7 is separated from the rest by a gap of \(7-5=2\) siblings, and it is well above the other values (0 to 5).

It is a potential outlier, separated by a gap. It should be mentioned in a description, and checked for a data-entry error.

Use tens digits as stems (4 through 8) and ones digits as leaves, in order.

Smallest 48, largest 83, with most values in the 60s and 70s.

(a) \(4+9+14=27\).

(b) \(3+2=5\) students, and \(\frac{5}{40}=12.5\%\).

(c) The tallest bar is 20 to under 30 minutes, with 14 students.

27 students; 12.5%; the 20-30 interval.

A histogram displays a quantitative variable. Its horizontal axis is a number line, so each interval runs directly into the next one. Gaps would suggest missing values.

Bars touch because the intervals are continuous on a numerical scale.

The bars rise to the right and the tail is toward the low scores.

Skewed left, unimodal, with the peak at the highest interval.

Tally each value into its interval.

Total: \(1+7+7+3+2=20\).

1, 7, 7, 3, 2.

There are two clear peaks, so the distribution is bimodal.

Bimodal; probably two groups with different typical heights (girls and boys) are mixed in one data set.

Divide each count by 40: 0.100, 0.225, 0.350, 0.200, 0.075, 0.050.

Dividing every count by the same number rescales the vertical axis only.

0.100, 0.225, 0.350, 0.200, 0.075, 0.050; the shape is unchanged.

(a) 48 bpm.

(b) The 7 row has leaves 0, 2, 4, 5, 9, so 5 athletes.

(c) \(83-48=35\) bpm.

48 bpm; 5 athletes; range 35 bpm.

With 50-point intervals the scores fall into only about 2 bars, which hides peaks, gaps, and skew.

The 50-point version hides the shape; 5- or 10-point intervals show it.

The tallest bar is 20 to 30 minutes, and the 20th and 21st students lie in that bar (\(4+9=13\) students are below 20, \(13+14=27\) are below 30), so the median is about 25 minutes. Times run from 0 to 60 minutes.

Center about 25 minutes; spread from 0 to 60 minutes (range about 60).

Order: 2.1, 2.5, 2.8, 2.9, 3.0, 3.1, 3.3, 3.4, 3.6, 3.8, 4.0, 9.6. Median: \(\frac{3.1+3.3}{2}=3.2\) inches.

Skewed right with a clear outlier at 9.6 inches; the center is about 3.2 inches and the other values range from 2.1 to 4.0 inches.

The dots cluster near 52 and trail off evenly on both sides, so the distribution is roughly symmetric and unimodal.

More than 54: 55, 56, 58, 60, which is \(4\) backpacks.

Roughly symmetric with a peak at 52; 4 backpacks.

Class A: most scores from 55 to 70, with 95 far above the rest (right tail, outlier). Class B: 58 to 74 with no unusual values and a roughly symmetric pattern.

Class A is skewed right with an outlier at 95 and a range of 40; Class B is roughly symmetric with a range of 16.

\(0.18\times 250=45\) workers.

Less than $14: \(0.07+0.15+0.18=0.40\).

45 workers; 40% earn less than $14.

A dotplot shows every value and works for small sets; with 600 values the dots would overlap and a histogram is clearer.

Dotplot for the 12 percentages, histogram for the 600 times.

(a) One peak at 10 to 15 with a slight tail to the right.

(b) \(10+5+1=16\) flights, \(\frac{16}{35}\approx 0.457\).

(c) The 18th value: \(2+6=8\), \(8+11=19\), so the 18th value is in 10 to 15.

Roughly symmetric, slightly right-skewed; 16/35 (about 45.7%); median in 10 to 15 minutes.

After correction, the Class A scores are 55, 60, 62, 64, 65, 65, 65, 66, 68, 70. The maximum is 70.

Range: \(70-55=15\).

The outlier disappears, the shape becomes roughly symmetric, and the range drops from 40 to 15.

The 7th of 13 ordered values is 67, so the median is 67 bpm.

Below 65: 48, 52, 55, 61, 63, 63, which is \(6\) athletes, and \(\frac{6}{13}\approx 46.2\%\).

Median 67 bpm; about 46.2% are below 65 bpm.