Math Problem Statement

Data was collected for 290 randomly selected 10-minute intervals. For each ten-minute interval, the number of people entering the atrium of a large mall were recorded. The data is summarized in the histogram below.

20 40 60 80 100 120 140 160 180 200 Number of People in 10 min Frequency [Graphs generated by this script: setBorder(54,40,20,5); initPicture(82,200,0,91);axes(1000,20,1,1000,20); fill="blue"; stroke="black";line([100,-1.82],[100,1.82]); text([100,0],"100","below");line([120,-1.82],[120,1.82]); text([120,0],"120","below");line([140,-1.82],[140,1.82]); text([140,0],"140","below");line([160,-1.82],[160,1.82]); text([160,0],"160","below");line([180,-1.82],[180,1.82]); text([180,0],"180","below");line([200,-1.82],[200,1.82]); text([200,0],"200","below");textabs([165,0],"Number of People in 10 min","above");textabs([0,115],"Frequency","right",90);rect([100,0],[120,90]);rect([120,0],[140,25]);rect([140,0],[160,67]);rect([160,0],[180,91]);rect([180,0],[200,17]);]

What is the class width for this histogram (and corresponding GFDT)? Note: Each class contains its lower class limit, but not its upper class limit.

Solution

To determine the class width for the histogram, we need to look at the difference between the lower class limits of any two consecutive classes.

Based on the information provided, the class limits are as follows:

  • The first class ranges from 100 to 120
  • The second class ranges from 120 to 140
  • The third class ranges from 140 to 160
  • The fourth class ranges from 160 to 180
  • The fifth class ranges from 180 to 200

The class width is calculated by subtracting the lower class limit of one class from the lower class limit of the next class:

Class Width=Lower class limit of second class−Lower class limit of first class\text{Class Width} = \text{Lower class limit of second class} - \text{Lower class limit of first class}

Class Width=120−100=20\text{Class Width} = 120 - 100 = 20

So, the class width for this histogram is 20.

Would you like more details, or do you have any questions?

Here are 5 related questions:

  1. How would you determine the midpoint of a class interval?
  2. What is the significance of the frequency in a histogram?
  3. How do you calculate the relative frequency from a histogram?
  4. What is the total number of observations represented in the histogram?
  5. How does the choice of class width affect the appearance of the histogram?

Tip: When analyzing histograms, always check the consistency of class intervals, as irregular widths can distort the data interpretation.

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Math Problem Analysis

Mathematical Concepts

Statistics
Histograms

Formulas

-

Theorems

-

Suitable Grade Level

High School

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