Math Problem Statement

Complete the frequency distribution using the classes: 10-14, 15-19, 20-24, 25-29, 30-34, 35-39 10, 12, 15, 18, 19, 15, 26 ,34, 25, 36, 39, 37, 26, 24, 25 ,21 ,20 ,10, 16, 18, 25, 34, 12, 15, 24, 38, 32, 25, 24, 16, 18, 19, 34, 38, 26, 22, 20, 10, 30, 16 What percent of the data values fall in the class 20-24?

Solution

Let's first create the frequency distribution table for the given data based on the classes provided:

Classes:

  • 10-14
  • 15-19
  • 20-24
  • 25-29
  • 30-34
  • 35-39

Data:

10, 12, 15, 18, 19, 15, 26, 34, 25, 36, 39, 37, 26, 24, 25, 21, 20, 10, 16, 18, 25, 34, 12, 15, 24, 38, 32, 25, 24, 16, 18, 19, 34, 38, 26, 22, 20, 10, 30, 16

Step 1: Count the frequency for each class.

  1. Class 10-14:
    Values: 10, 12, 12, 10, 10
    Frequency: 5

  2. Class 15-19:
    Values: 15, 18, 19, 15, 18, 16, 18, 15, 16, 18, 19
    Frequency: 11

  3. Class 20-24:
    Values: 21, 20, 24, 24, 20, 24, 22
    Frequency: 7

  4. Class 25-29:
    Values: 26, 25, 26, 25, 25, 25, 26
    Frequency: 7

  5. Class 30-34:
    Values: 34, 34, 34, 32, 30
    Frequency: 5

  6. Class 35-39:
    Values: 36, 39, 37, 38, 38
    Frequency: 5

Step 2: Calculate the total number of data values.

Total frequency = 5 + 11 + 7 + 7 + 5 + 5 = 40

Step 3: Calculate the percentage of data values that fall in the class 20-24.

Percentage=(Frequency of Class 20-24Total Frequency)×100=(740)×100=17.5%\text{Percentage} = \left(\frac{\text{Frequency of Class 20-24}}{\text{Total Frequency}}\right) \times 100 = \left(\frac{7}{40}\right) \times 100 = 17.5\%

Answer: 17.5% of the data values fall in the class 20-24.


Do you want more details or have any questions?

Here are 5 related questions:

  1. What is the relative frequency of the class 15-19?
  2. How do you calculate the cumulative frequency for these classes?
  3. What is the mode of the data set?
  4. Can you construct a histogram based on this frequency distribution?
  5. What is the mean of the data set?

Tip: When calculating percentages for a specific class, always ensure that the total frequency is accurate to avoid miscalculations.

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution
Percentage Calculation

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12