Q 65. - The Practice of Statistics for AP

Question

Comparing AP scores The table below gives the distribution of grades earned by students taking the AP Calculus AB and AP Statistics exams in $2009$

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

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

Step-by-Step Solution

Answer

Part (b) 

• Calculus AB students is two-peaked.
• Statistics students is one-peaked.

Part (a) Calculus AB 

AP Statistics 

Part (a) Step 1: Given information

Given data : 

			Grade
No. of exams		5	4	3	2	1
Calculus AB	230588	52921	43140	41204	35843	57480
Statistics	116,876	14,353	26,050	28276	22283	25914

Part (a) Step 2: Concept

A histogram is a common graphing tool. It's utilized to summarize discrete or continuous data that's measured on an interval scale. It's widely used to show the key properties of a data distribution in a user-friendly style.

Part (a) Step 3: Explanation

The $\%$ is calculated by dividing the number of rows in the table by the total number of rows (number of exams). 

Because the Grade is categorical, you should use a bar graph (histogram requires that the variable is numerical).

The bars must be the same width and height, and the percentage of exams must be the same. 

CALCULUS AB 

STATISTIC

The comparison of the two graphs occurs in the next part of the question.

Part (b) Step 1: Explanation

The number of students who did Calculus AB is significantly higher than the number who took statistics. The majority of students in Statistics have a grade of $3$, but the majority of students in Calculus AB earn a grade of $1$ or $5$.

Calculus AB students have a two-peaked distribution, whereas statistics students have a one-peaked, generally bell-shaped distribution.