Which of the following questions would be good to display on a histogram?
Select all that apply.
A. How many siblings do the students in your class have?
B. What is the distance that the students in the sixth grade live from school?
C. What are the favorite desserts of students in the sixth grade?
D. What are the test scores of the state test for math for the sixth grade students in your school?
E. What are the times of the students in your class for the 50 yard dash?
The correct answer and explanation is:
The correct answers are B, D, and E.
Explanation:
A histogram is best used for displaying continuous or discrete numerical data where the data points are grouped into intervals or bins. The purpose is to show the distribution of data, allowing one to observe patterns such as central tendency, spread, and any possible skewness or outliers.
- B. What is the distance that the students in the sixth grade live from school?
This is continuous numerical data that can be represented by intervals (e.g., distances ranging from 0-1 km, 1-2 km, etc.). A histogram would allow you to see the distribution of how far students live from school, highlighting trends such as whether most students live close or far from school. - D. What are the test scores of the state test for math for the sixth grade students in your school?
This is also continuous numerical data. Test scores can be broken into ranges (e.g., 50-60, 60-70, etc.) to show how students are performing overall. A histogram would reveal patterns such as whether most students are clustered in a specific score range, or if the scores are spread out. - E. What are the times of the students in your class for the 50-yard dash?
These are continuous data points related to speed or time, which can also be grouped into intervals (e.g., 5-6 seconds, 6-7 seconds, etc.). A histogram would help to visualize whether most students are running within a particular time range.
Why the other options do not work well for histograms:
- A. How many siblings do the students in your class have?
This is categorical, not continuous. While it could be represented in a bar chart, a histogram is not suitable because it involves counting distinct categories (e.g., 1 sibling, 2 siblings, etc.), not continuous data. - C. What are the favorite desserts of students in the sixth grade?
This is also categorical data (e.g., chocolate cake, ice cream, pie), and again, would be better suited for a bar chart rather than a histogram.
Histograms are used to represent data distributions for continuous or discrete numerical variables, so the questions involving numerical data grouped into ranges or intervals are the best fit.