Q 67. - The Practice of Statistics for AP

Question

Student survey A survey of a large high school class asked the following questions:

(i) Are you female or male? (In the data, male = $0$, female = $1$)

(ii) Are you right-handed or left-handed? (In the data, right = $0$, left = $1$)

(iii) What is your height in inches?

(iv) How many minutes do you study on a typical weeknight?

The figure below shows histograms of the student responses, in scrambled order and without scale markings. Which histogram goes with each variable? Explain your reasoning.

Step-by-Step Solution

Answer

Histogram (c) goes with question (i)

Histogram (d) goes with question (iv)

Histogram (b) goes with question (ii)

Histogram (a) goes with question (iii)

Step 1: Given information

(i)Female or male (In the data, male = $0$, female = $1$)

(ii)Right-handed or left -handed (In the data, right = $0$, left = $1$)

(iii)Height in inches.

(iv)The study time at weeknight. 

Step 2: Concept

A histogram is a graphing tool that is extensively used. It's used to summarise discrete or continuous data measured on a scale of one to ten. It's a standard way of exhibiting essential data distribution aspects in an easy-to-understand format. 

Step 3: Explanation

The histogram (a) corresponds to question (iii), and it depicts the distribution of height in inches, since most of the respondents from a large high school class belong to the same group, and only a few are taller than average.

The histogram (b) corresponds to question (ii), indicating whether a pupil in a large high school class is right- or left-handed. People are normally right-handed since right is 0 and left is 1. The histogram (b) reveals that the majority of them are right-handed, which is in line with the general trend, and that only a handful are left-handed.

The histogram (c) corresponds to query I in that it categorizes individuals from a large high school class by gender. There are more ladies in the class than males because male = 0 and female = 1.

The histogram (d) corresponds to question (iv), which is how much time each student in a large high school class spends on a typical weekday. Variations in the distribution are conceivable owing to differences in study duration. The histogram's distribution is symmetric.