Sure, let's break down the formulas for finding the mean in different types of series:
1. Mean of Individual Series
For an individual series, the mean ([tex]\(\bar{x}\)[/tex]) is calculated as:
[tex]\[
\bar{x} = \frac{\text{Sum of all observations}}{\text{Number of observations}}
\][/tex]
This is a straightforward average where you add up all the values and divide by the number of values.
2. Mean of Discrete Data
For discrete data, where the observations come with frequencies, the mean is given by:
[tex]\[
\bar{x} = \frac{\Sigma (f \cdot x)}{N}
\][/tex]
Here:
- [tex]\(f\)[/tex] is the frequency of each observation [tex]\(x\)[/tex],
- [tex]\(N\)[/tex] is the total number of observations.
You multiply each observation by its frequency, sum all those products, and then divide by the total number of observations.
3. Mean of Continuous Data
For continuous data, where the data is grouped into intervals, the formula for the mean is:
[tex]\[
\bar{x} = \frac{\Sigma (f \cdot \bar{x})}{N}
\][/tex]
Here:
- [tex]\(f\)[/tex] is the frequency of each class interval,
- [tex]\(\bar{x}\)[/tex] is the midpoint of each class interval,
- [tex]\(N\)[/tex] is the total number of observations.
You calculate the midpoint of each class interval, multiply by the frequency of the interval, sum all these products, and divide by the total number of observations.
These formulas are essential tools in statistics for summarizing data and understanding its central tendency.
