Math Problem Statement

Given the relative frequency table below, which of the following is the corresponding cumulative relative frequency table?

Solution

To find the corresponding cumulative relative frequency table, we will calculate the cumulative frequency for each value in the table by summing the relative frequencies progressively.

Here is how we calculate the cumulative frequencies:

  1. For the first value (3), the cumulative frequency is just its relative frequency:
    Cumulative frequency for 3 = 0.4.

  2. For the second value (4), we add the previous cumulative frequency (for 3) to the relative frequency for 4:
    Cumulative frequency for 4 = 0.4 + 0.1 = 0.5.

  3. For the third value (5), we add the cumulative frequency for 4 to the relative frequency for 5:
    Cumulative frequency for 5 = 0.5 + 0.3 = 0.8.

  4. For the fourth value (6), we add the cumulative frequency for 5 to the relative frequency for 6:
    Cumulative frequency for 6 = 0.8 + 0.2 = 1.0.

So the cumulative relative frequency table is:

ValueCumulative Frequency
30.4
40.5
50.8
61.0

Would you like further details or explanation?

Here are five related questions to further explore the concept:

  1. How does the cumulative relative frequency differ from relative frequency?
  2. Can cumulative frequencies ever decrease?
  3. What is the importance of a cumulative frequency table in data analysis?
  4. How would you interpret a cumulative frequency of 1.0 in this table?
  5. How would the table change if the relative frequencies summed to less than 1?

Tip: The last cumulative relative frequency should always equal 1 if the table covers the entire dataset.

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Math Problem Analysis

Mathematical Concepts

Statistics
Cumulative Frequency
Relative Frequency

Formulas

Cumulative Frequency = Sum of relative frequencies up to a specific value

Theorems

Cumulative Frequency Theorem

Suitable Grade Level

Grades 6-8