Math Problem Statement

Consider the following frequency table representing the distribution of cost of a paperback book (in dollars).

Cost of a Paperback Book (in Dollars)ClassFrequency

6.1–6.96.1–6.9

1414

7.0–7.87.0–7.8

44

7.9–8.77.9–8.7

1515

8.8–9.68.8–9.6

99

9.7–10.59.7–10.5

1010

Copy Data

Step 1 of 2 :

Determine the midpoint for the fifth class.

Solution

To determine the midpoint for the fifth class, we use the following formula for the midpoint MM of a class interval:

M=Lower Class Limit+Upper Class Limit2M = \frac{\text{Lower Class Limit} + \text{Upper Class Limit}}{2}

For the fifth class (9.7–10.5):

  • Lower class limit = 9.7
  • Upper class limit = 10.5

Now, calculate the midpoint:

M=9.7+10.52=20.22=10.1M = \frac{9.7 + 10.5}{2} = \frac{20.2}{2} = 10.1

Thus, the midpoint for the fifth class is 10.110.1 dollars.

Would you like further details on this process, or do you have any other questions?


Here are 5 related questions:

  1. How do we calculate the midpoint for other classes?
  2. What is the purpose of finding midpoints in frequency distribution?
  3. How can we find the mean cost of a book using midpoints and frequencies?
  4. What is the difference between the midpoint and the class boundary?
  5. How does the width of a class interval affect the midpoint?

Tip: Always double-check that you're adding the correct class limits when calculating midpoints to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution
Midpoint Calculation

Formulas

Midpoint formula: M = (Lower Class Limit + Upper Class Limit) / 2

Theorems

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Suitable Grade Level

Grades 9-12