Thank you for visiting If the mean of a frequency distribution is 39 4 and the total of frequencies is 100 what is the total of the products of. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
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.
Thank you for reading the article If the mean of a frequency distribution is 39 4 and the total of frequencies is 100 what is the total of the products of. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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