Question

AP® exam scores The table gives the distribution of grades earned by students taking the AP® Calculus AB and AP® Statistics exams in 2016

Part (a). Make an appropriate graphical display to compare the grade distributions for AP® Calculus AB and AP® Statistics.

Part (b). Write a few sentences comparing the two distributions of exam grades.

Short answer

Part (a)

Statistics

Calculus AB

Part (b)

Both distributions seem roughly symmetric.

There do not appear to be any outliers.

The distributions' center appears to be around 3.

The spread is the same for both distributions.

Step-by-step solution

Part (a) Step 1 Given information. 

The table gives the distribution of grades earned by students taking the AP® Calculus AB and AP® Statistics exams in 2016

Part (a) Step 2  A suitable graphical display for comparing grade distributions

Because the number of students who took AP Calculus AB and AP Statistics is not the same, comparing two frequency histograms of the corresponding distributions is not appropriate, and we will need to determine the relative frequency histograms.

The relative frequencies can then be calculated by dividing the frequencies in the above table by the row totals.

	5	4	3	2	1
Calculus AB	$\frac{76,467}{308,215}\approx 0.2482$	$\frac{53,467}{308,215}\approx 0.1735$	$\frac{53,533}{308,215}\approx 0.17437$	$\frac{30,017}{308,215}\approx 0.0974$	$\frac{94,712}{308,215}\approx 0.3073$
Statistics	$\frac{29,627}{206,563}\approx 0.1434$	$\frac{44,844}{206,563}\approx 0.2171$	$\frac{51,367}{206,563}\approx 0.2487$	$\frac{32,120}{206,563}\approx 0.1555$	$\frac{48,565}{206,563}\approx 0.2351$

The width of the bar must be the same, and the bars must be horizontally bounded by the class boundaries.

The height of the bars must be proportional to the relative frequency.

Calculus AB

Statistics graph

Part (b) Step 1 A few sentences comparing the two exam grade distributions.

Both distributions appear to be roughly symmetric because neither has a tail of smaller bars on either side of the histogram.

Because there are no gaps in the histograms, there appear to be no outliers.

Because the Calculus AB distributions have the highest bars at 1 and 5 (while 3 is exactly in the middle of 1 and 5), the center of the distributions appears to be roughly at 3, while Statistic has the highest bar at 3.

Because the Calculus AB distributions have the highest bars at 1 and 5 (while 3 is exactly in the middle of 1 and 5), the center of the distributions appears to be roughly at 3, while Statistic has the highest bar at 3.

Because both distributions accept values ranging from 1 to 5, they have the same spread.

As a result:

Both distributions seem roughly symmetric.

There do not appear to be any outliers.

The distributions' center appears to be around 3.

The spread is the same for both distributions.