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the mean of the values of 1,2,3....n with respective frequency x, 2x,3x...nx is
? Related: Statistical Description of Data
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the mean of the values of 1,2,3....n with respective frequency x, 2x,3...
Understanding the Mean of Frequency Distribution
The mean of a frequency distribution is a crucial statistical measure that helps summarize a set of data, especially when different values have different frequencies. In this case, we have values from 1 to n with frequencies increasing in a linear pattern: x, 2x, 3x,..., nx.
Calculating the Mean
To find the mean, we use the formula for the weighted mean:
Where:
- f = frequency of each value
- x = corresponding value
Frequency and Values
Given the values and their respective frequencies:
Summation Components
1. **Total Frequency (Σf)**:
- Calculate the total frequency:
2. **Weighted Sum (Σ(f * x))**:
- Calculate the weighted sum:
Final Mean Formula
Substituting the summation results into the mean formula gives:
This result indicates that the mean of the frequency distribution is directly related to the maximum value n in the dataset. Understanding this relationship is vital in statistical data analysis.
The mean of a frequency distribution is a crucial statistical measure that helps summarize a set of data, especially when different values have different frequencies. In this case, we have values from 1 to n with frequencies increasing in a linear pattern: x, 2x, 3x,..., nx.
Calculating the Mean
To find the mean, we use the formula for the weighted mean:
- Mean (μ) = (Σ(f * x)) / Σf
Where:
- f = frequency of each value
- x = corresponding value
Frequency and Values
Given the values and their respective frequencies:
- Values: 1, 2, 3, ..., n
- Frequencies: x, 2x, 3x, ..., nx
Summation Components
1. **Total Frequency (Σf)**:
- Calculate the total frequency:
- Σf = x + 2x + 3x + ... + nx = x(1 + 2 + 3 + ... + n) = x(n(n + 1)/2)
2. **Weighted Sum (Σ(f * x))**:
- Calculate the weighted sum:
- Σ(f * x) = 1*x + 2*2x + 3*3x + ... + n*nx
- Σ(f * x) = x(1^2 + 2^2 + 3^2 + ... + n^2) = x(n(n + 1)(2n + 1)/6)
Final Mean Formula
Substituting the summation results into the mean formula gives:
- Mean (μ) = (x(n(n + 1)(2n + 1)/6)) / (x(n(n + 1)/2))
- Mean (μ) = (2n + 1) / 3
This result indicates that the mean of the frequency distribution is directly related to the maximum value n in the dataset. Understanding this relationship is vital in statistical data analysis.
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the mean of the values of 1,2,3....n with respective frequency x, 2x,3x...nx is Related: Statistical Description of Data?
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