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In a frequency distribution, how is the mean calculated?
- a)By multiplying each value by its frequency and dividing by total frequency.
- b)By summing all values and dividing by the frequency count.
- c)By taking the middle value of the frequency.
- d)By identifying the most common frequency.
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a frequency distribution, how is the mean calculated?a)By multiplyi...
Understanding Frequency Distribution Mean
In statistics, the mean (or average) is a useful measure that summarizes a set of values. When working with a frequency distribution, the mean is calculated differently than with a simple list of numbers.
Calculation Method
To find the mean in a frequency distribution, follow these steps:
- Multiply Each Value by Its Frequency: For each unique value in the dataset, you multiply the value by how many times it occurs (its frequency). This gives you the total contribution of each value to the overall sum.
- Sum All Contributions: Once you have the products from the previous step, you sum all of these contributions together. This provides the overall total of all values in the dataset.
- Divide by Total Frequency: Finally, you divide this total sum by the total frequency (the sum of all frequencies). This gives you the mean of the distribution.
Example
Consider a simple frequency distribution:
| Value | Frequency |
|-------|-----------|
| 1 | 2 |
| 2 | 3 |
| 3 | 5 |
The calculation would be:
- (1 * 2) + (2 * 3) + (3 * 5) = 2 + 6 + 15 = 23
The total frequency = 2 + 3 + 5 = 10.
Thus, the mean = 23 / 10 = 2.3.
Conclusion
Therefore, the correct answer is option 'A': the mean is calculated by multiplying each value by its frequency and then dividing by the total frequency. This method accurately reflects the contribution of each value based on its occurrence in the dataset.
In statistics, the mean (or average) is a useful measure that summarizes a set of values. When working with a frequency distribution, the mean is calculated differently than with a simple list of numbers.
Calculation Method
To find the mean in a frequency distribution, follow these steps:
- Multiply Each Value by Its Frequency: For each unique value in the dataset, you multiply the value by how many times it occurs (its frequency). This gives you the total contribution of each value to the overall sum.
- Sum All Contributions: Once you have the products from the previous step, you sum all of these contributions together. This provides the overall total of all values in the dataset.
- Divide by Total Frequency: Finally, you divide this total sum by the total frequency (the sum of all frequencies). This gives you the mean of the distribution.
Example
Consider a simple frequency distribution:
| Value | Frequency |
|-------|-----------|
| 1 | 2 |
| 2 | 3 |
| 3 | 5 |
The calculation would be:
- (1 * 2) + (2 * 3) + (3 * 5) = 2 + 6 + 15 = 23
The total frequency = 2 + 3 + 5 = 10.
Thus, the mean = 23 / 10 = 2.3.
Conclusion
Therefore, the correct answer is option 'A': the mean is calculated by multiplying each value by its frequency and then dividing by the total frequency. This method accurately reflects the contribution of each value based on its occurrence in the dataset.
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Community Answer
In a frequency distribution, how is the mean calculated?a)By multiplyi...
To calculate the mean in a frequency distribution:
- Multiply each value by its corresponding frequency.
- Add all these products together.
- Divide the total by the sum of the frequencies.
This method provides an accurate calculation of the mean based on the distribution of values and their frequencies.
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