Math Problem Statement

The user submitted a frequency table showing the number of movies watched by individuals and requires calculations for relative and cumulative relative frequencies.

Solution

The table provided shows frequencies for different numbers of movies, and it requires calculations for both relative frequency and cumulative relative frequency. Let's proceed step by step.

Step 1: Calculate the Total Frequency

The total frequency is the sum of all individual frequencies: 5+10+5+4+1=255 + 10 + 5 + 4 + 1 = 25 This total is important for determining the relative frequency.

Step 2: Calculate the Relative Frequency

Relative frequency is calculated as the frequency for each category divided by the total frequency. Let's compute it for each category:

  • For 0 movies: 525=0.2\frac{5}{25} = 0.2
  • For 1 movie: 1025=0.4\frac{10}{25} = 0.4
  • For 2 movies: 525=0.2\frac{5}{25} = 0.2
  • For 3 movies: 425=0.16\frac{4}{25} = 0.16
  • For 4 movies: 125=0.04\frac{1}{25} = 0.04

Step 3: Calculate the Cumulative Relative Frequency

Cumulative relative frequency is calculated by adding up the relative frequencies progressively. Let's compute it:

  • For 0 movies: 0.20.2 (same as the relative frequency)
  • For 1 movie: 0.2+0.4=0.60.2 + 0.4 = 0.6
  • For 2 movies: 0.6+0.2=0.80.6 + 0.2 = 0.8
  • For 3 movies: 0.8+0.16=0.960.8 + 0.16 = 0.96
  • For 4 movies: 0.96+0.04=1.000.96 + 0.04 = 1.00

Completed Table:

# of MoviesFrequencyRelative FrequencyCumulative Relative Frequency
050.20.2
1100.40.6
250.20.8
340.160.96
410.041.00

Would you like more details or any clarifications?

Here are 5 related questions:

  1. What does the cumulative relative frequency represent?
  2. How do we interpret a relative frequency of 0.4?
  3. How would the table change if the frequency for 1 movie increased?
  4. What happens to cumulative relative frequency if the total frequency is underestimated?
  5. How could this data be represented in a graph?

Tip: Always check that the cumulative relative frequency sums to 1 (or very close to 1 due to rounding) to ensure calculations are correct.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Relative Frequency
Cumulative Frequency

Formulas

Relative Frequency = (Frequency / Total Frequency)
Cumulative Relative Frequency = Sum of all previous relative frequencies including the current one

Theorems

Law of Total Probability

Suitable Grade Level

Grades 6-8