Math Problem Statement
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: 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:
- For 1 movie:
- For 2 movies:
- For 3 movies:
- For 4 movies:
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: (same as the relative frequency)
- For 1 movie:
- For 2 movies:
- For 3 movies:
- For 4 movies:
Completed Table:
# of Movies | Frequency | Relative Frequency | Cumulative Relative Frequency |
---|---|---|---|
0 | 5 | 0.2 | 0.2 |
1 | 10 | 0.4 | 0.6 |
2 | 5 | 0.2 | 0.8 |
3 | 4 | 0.16 | 0.96 |
4 | 1 | 0.04 | 1.00 |
Would you like more details or any clarifications?
Here are 5 related questions:
- What does the cumulative relative frequency represent?
- How do we interpret a relative frequency of 0.4?
- How would the table change if the frequency for 1 movie increased?
- What happens to cumulative relative frequency if the total frequency is underestimated?
- 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.
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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
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