Question

a survey was given to 84 students at a local high school, asking how many minutes it takes them to commute to school. the results are summarized in the table below. construct and label a frequency histogram of the data with an appropriate scale.

minutes	num. of students
20 - 39	45
40 - 59	21
60 - 79	3

Explanation:

Step1: Determine x - axis and y - axis

The x - axis will represent the time intervals (minutes) and the y - axis will represent the number of students (frequency).

Step2: Choose a scale for the y - axis

The highest frequency is 45. We can choose a scale for the y - axis such that it goes up to at least 45. For example, we can use intervals of 5 (0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50).

Step3: Draw rectangles

For the interval 0 - 19, draw a rectangle with base from 0 to 19 on the x - axis and height corresponding to 15 on the y - axis.
For the interval 20 - 39, draw a rectangle with base from 20 to 39 on the x - axis and height corresponding to 45 on the y - axis.
For the interval 40 - 59, draw a rectangle with base from 40 to 59 on the x - axis and height corresponding to 21 on the y - axis.
For the interval 60 - 79, draw a rectangle with base from 60 to 79 on the x - axis and height corresponding to 3 on the y - axis.

Step4: Label the histogram

Label the x - axis as "Minutes" and the y - axis as "Number of Students". Give the histogram a title, for example, "Commute Time of High - School Students".

Since this is a construction task and not a numerical answer, we have provided the steps to construct the histogram. If you were to actually draw it on graph paper or using a software, you would follow these steps.

Answer:

Step1: Determine x - axis and y - axis

The x - axis will represent the time intervals (minutes) and the y - axis will represent the number of students (frequency).

Step2: Choose a scale for the y - axis

The highest frequency is 45. We can choose a scale for the y - axis such that it goes up to at least 45. For example, we can use intervals of 5 (0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50).

Step3: Draw rectangles

For the interval 0 - 19, draw a rectangle with base from 0 to 19 on the x - axis and height corresponding to 15 on the y - axis.
For the interval 20 - 39, draw a rectangle with base from 20 to 39 on the x - axis and height corresponding to 45 on the y - axis.
For the interval 40 - 59, draw a rectangle with base from 40 to 59 on the x - axis and height corresponding to 21 on the y - axis.
For the interval 60 - 79, draw a rectangle with base from 60 to 79 on the x - axis and height corresponding to 3 on the y - axis.

Step4: Label the histogram

Label the x - axis as "Minutes" and the y - axis as "Number of Students". Give the histogram a title, for example, "Commute Time of High - School Students".

Since this is a construction task and not a numerical answer, we have provided the steps to construct the histogram. If you were to actually draw it on graph paper or using a software, you would follow these steps.