Math Problem Statement

Complete the grouped relative frequency distribution for the data, using a class width of 4. The table consists of ranges such as 0 to 3 hours, 4 to 7 hours, etc. Calculate the relative frequency, rounded to the nearest hundredth.

Solution

The image you uploaded involves constructing a grouped relative frequency distribution from survey data.

Steps to calculate the missing relative frequency:

  1. Total number of responses: 18 (from the given instructions).
  2. Class intervals: These intervals are divided into ranges such as:
    • 0 to 3 hours (relative frequency: 0.11)
    • 4 to 7 hours (relative frequency: 0.44)
    • 8 to 11 hours (relative frequency: 0.33)
    • 12 to 15 hours (relative frequency: 0.06)
    • 16 to 19 hours (relative frequency: 0.06)

To calculate the missing value, we first check if the total relative frequency sums to 1, as required in a frequency distribution.

  1. Sum of given relative frequencies:
    • 0.11+0.44+0.33+0.06+0.06=10.11 + 0.44 + 0.33 + 0.06 + 0.06 = 1

Therefore, the total relative frequency already sums to 1, which means the table is correctly filled out.

Missing Relative Frequency:

  • The missing relative frequency is 0.06, based on the table setup.

Let me know if you'd like further details or additional assistance!

Here are 5 follow-up questions you might explore:

  1. How do you calculate relative frequency from raw data?
  2. What is the purpose of using grouped data in statistics?
  3. Can relative frequencies be greater than 1?
  4. How is cumulative relative frequency calculated?
  5. Why is the sum of relative frequencies always equal to 1?

Tip: Always ensure that the sum of all relative frequencies equals 1 to verify correctness in frequency distributions.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Relative Frequency
Grouped Data
Descriptive Statistics

Formulas

Relative Frequency = (Class Frequency / Total Frequency)

Theorems

Relative Frequency Distribution

Suitable Grade Level

Grades 9-12