Frequency Distribution Formula
There are various formulas which can be learned in the context of Frequency Distribution, one such formula is the coefficient of variation. This formula for Frequency Distribution is discussed below in detail.
Coefficient of Variation
We can use mean and standard deviation to describe the dispersion in the values. But sometimes while comparing the two series or frequency distributions becomes a little hard as sometimes both have different units.
The coefficient of Variation is defined as,
[Tex]\bold{\frac{\sigma}{\bar{x}} \times 100} [/Tex]
Where,
- σ represents the standard deviation
- [Tex]\bold{\bar{x}}[/Tex] represents the mean of the observations
Note: Data with greater C.V. is said to be more variable than the other. The series having lesser C.V. is said to be more consistent than the other.
Comparing Two Frequency Distributions with the Same Mean
We have two frequency distributions. Let’s say [Tex]\sigma_{1} \text{ and } \bar{x}_1[/Tex] are the standard deviation and mean of the first series and [Tex]\sigma_{2} \text{ and } \bar{x}_2[/Tex] are the standard deviation and mean of the second series. The Coefficeint of Variation(CV) is calculated as follows
C.V of first series = [Tex]\frac{\sigma_1}{\bar{x}_1} \times 100 [/Tex]
C.V of second series = [Tex]\frac{\sigma_2}{\bar{x}_2} \times 100 [/Tex]
We are given that both series have the same mean, i.e.,
[Tex]\bar{x}_2 = \bar{x}_1 = \bar{x} [/Tex]
So, now C.V. for both series are,
C.V. of the first series = [Tex] \frac{\sigma_1}{\bar{x}} \times 100[/Tex]
C.V. of the second series = [Tex]\frac{\sigma_2}{\bar{x}} \times 100[/Tex]
Notice that now both series can be compared with the value of standard deviation only. Therefore, we can say that for two series with the same mean, the series with a larger deviation can be considered more variable than the other one.
Frequency Distribution – Table, Graphs, Formula
Frequency Distribution is a tool in statistics that helps us organize the data and also helps us reach meaningful conclusions. It tells us how often any specific values occur in the dataset.
A frequency distribution represents the pattern of how frequently each value of a variable appears in a dataset. It shows the number of occurrences for each possible value within the dataset.
Let’s learn about Frequency Distribution including its definition, graphs, solved examples, and frequency distribution table in detail.
Table of Content
- What is Frequency Distribution in Statistics?
- Frequency Distribution Graphs
- Frequency Distribution Table
- Types of Frequency Distribution Table
- Frequency Distribution Table for Grouped Data
- Frequency Distribution Table for Ungrouped Data
- Types of Frequency Distribution
- Grouped Frequency Distribution
- Ungrouped Frequency Distribution
- Relative Frequency Distribution
- Cumulative Frequency Distribution
- Frequency Distribution Curve
- Frequency Distribution Formula
- Frequency Distribution Examples