Math Problem Statement

Data was collected for 76 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 table below. Number of Guests Frequency 100 – 104 28 105 – 109 13 110 – 114 17 115 – 119 5 120 – 124 13 What is the class width?

Solution

To determine the class width, we calculate the difference between the upper and lower boundaries of any one class.

For this data set:

  • The first class is 100104100 - 104.
  • The lower boundary is 100.
  • The upper boundary is 104.

The class width is calculated as:

Class Width=Upper BoundaryLower Boundary+1\text{Class Width} = \text{Upper Boundary} - \text{Lower Boundary} + 1

So,

Class Width=104100+1=5\text{Class Width} = 104 - 100 + 1 = 5

Therefore, the class width is 5.

Would you like more details or have any other questions?

Here are 5 related questions you might find interesting:

  1. How do you determine the number of classes in a frequency distribution?
  2. What is the importance of selecting an appropriate class width in a frequency distribution?
  3. How would changing the class width affect the appearance of a histogram?
  4. Can you calculate the midpoint of each class?
  5. What is the difference between class width and class interval?

Tip: When working with frequency distributions, always check that the classes are mutually exclusive and collectively exhaustive to avoid any overlap or missing data.

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution

Formulas

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Theorems

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Suitable Grade Level

Grades 10-12