Q 50. - The Practice of Statistics for AP

Question

Basketball playoffs Here are the scores of the games played in the California Division I-AAA high school basketball playoffs 

On the same day, the final scores of games in the Division

V-AA were

(a) Construct a back-to-back stem plot to compare the points scored by the $32$ teams in the Division I-AAA playoffs and the $24$ teams in the Division V-AA

playoffs.

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

Step-by-Step Solution

Answer

Part (b) The distribution of I-AAA is more symmetric as compare to V-AA.

Part (a) 

Part (a) Step 1: The given information

The table is 

71-38	52-47	55-53	76-65	77-63	65-63	68-54	64-62
87-47	64-56	78-64	58-51	91-74	71-41	67-62	106-46

98-45	67-44	74-60	96-54	92-72	93-46
98-67	62-37	37-36	69-44	86-66	66-58

Part (a) Step 2: Concept

The peak of the dot plot is at this means that during that season, the team's most common number of goals scored in games (known as the mode) was The United States women's soccer team scored between one and five goals in the majority of its games. The distribution, however, has a large tail to the right.

Part (a) Step 3: Explanation

The following is a stem plot for I-AAA high school payoffs: 

The following is a stem plot for the V-AA playoffs: 

The stem plot compares the points scored by $32$ Division I-AAA teams and $24$ Division V-AA teams in the playoffs. 

Thus, a stem plot is made to compare the points.

Part (b) Step 1: Explanation

In comparison to V-AA, the distribution of I-AAA is more symmetric, as seen by the stem plot. In the 1-AAA distribution, there is only one peak. It has a single peak and is called unimodal. The V-AA distribution is asymmetric in nature. It is bimodal and has two peaks.