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Answer :
To find the total of the products of frequencies of the sets by their centers, we use the formula for the mean of a frequency distribution. Here's a step-by-step breakdown:
1. Understand the Problem:
- We have a frequency distribution with a mean of 39.4.
- The total of all frequencies is given as 100.
2. Formula for Mean of a Frequency Distribution:
- The mean is calculated by dividing the total sum of the products of frequencies and their centers by the total number of frequencies.
3. Set Up the Equation:
- Let's denote the total of the products of frequencies and their centers as [tex]\( \Sigma f_i \cdot x_i \)[/tex].
- The formula for the mean is:
[tex]\[
\text{Mean} = \frac{\Sigma f_i \cdot x_i}{\text{Total Frequencies}}
\][/tex]
4. Substitute Given Values:
- Substitute the given mean (39.4) and the total frequencies (100) into the formula:
[tex]\[
39.4 = \frac{\Sigma f_i \cdot x_i}{100}
\][/tex]
5. Solve for [tex]\( \Sigma f_i \cdot x_i \)[/tex]:
- Multiply both sides by the total number of frequencies to find the total of the products:
[tex]\[
\Sigma f_i \cdot x_i = 39.4 \times 100
\][/tex]
[tex]\[
\Sigma f_i \cdot x_i = 3940
\][/tex]
Therefore, the total of the products of frequencies of the sets by their centers is 3940.
1. Understand the Problem:
- We have a frequency distribution with a mean of 39.4.
- The total of all frequencies is given as 100.
2. Formula for Mean of a Frequency Distribution:
- The mean is calculated by dividing the total sum of the products of frequencies and their centers by the total number of frequencies.
3. Set Up the Equation:
- Let's denote the total of the products of frequencies and their centers as [tex]\( \Sigma f_i \cdot x_i \)[/tex].
- The formula for the mean is:
[tex]\[
\text{Mean} = \frac{\Sigma f_i \cdot x_i}{\text{Total Frequencies}}
\][/tex]
4. Substitute Given Values:
- Substitute the given mean (39.4) and the total frequencies (100) into the formula:
[tex]\[
39.4 = \frac{\Sigma f_i \cdot x_i}{100}
\][/tex]
5. Solve for [tex]\( \Sigma f_i \cdot x_i \)[/tex]:
- Multiply both sides by the total number of frequencies to find the total of the products:
[tex]\[
\Sigma f_i \cdot x_i = 39.4 \times 100
\][/tex]
[tex]\[
\Sigma f_i \cdot x_i = 3940
\][/tex]
Therefore, the total of the products of frequencies of the sets by their centers is 3940.
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