Frequency Distribution Examples
Example 1: Suppose we have a series, with a mean of 20 and a variance is 100. Find out the Coefficient of Variation.
Solution:
We know the formula for Coefficient of Variation,
[Tex]\frac{\sigma}{\bar{x}} \times 100 [/Tex]
Given mean [Tex]\bar{x}[/Tex] = 20 and variance [Tex]\sigma^2[/Tex] = 100.
Substituting the values in the formula,
[Tex]\frac{\sigma}{\bar{x}} \times 100 \\ = \frac{20}{\sqrt{100}} \times 100 \\ = \frac{20}{10} \times 100 \\ = 200 [/Tex]
Example 2: Given two series with Coefficients of Variation 70 and 80. The means are 20 and 30. Find the values of standard deviation for both series.
Solution:
In this question we need to apply the formula for CV and substitute the given values.
Standard Deviation of first series.
[Tex]C.V = \frac{\sigma}{\bar{x}} \times 100 \\ 70 = \frac{\sigma}{20} \times 100 \\ 1400 = \sigma \times 100 \\ 14 = \sigma [/Tex]
Thus, the standard deviation of first series = 14
Standard Deviation of second series.
[Tex]C.V = \frac{\sigma}{\bar{x}} \times 100 \\ 80 = \frac{\sigma}{30} \times 100 \\ 2400 = \sigma \times 100 \\ 24 = \sigma [/Tex]
Thus, the standard deviation of first series = 24
Example 3: Draw the frequency distribution table for the following data:
2, 3, 1, 4, 2, 2, 3, 1, 4, 4, 4, 2, 2, 2
Solution:
Since there are only very few distinct values in the series, we will plot the ungrouped frequency distribution.
Value Frequency 1
2
2
6
3
2
4
4
Total
14
Example 4: The table below gives the values of temperature recorded in Hyderabad for 25 days in summer. Represent the data in the form of less-than-type cumulative frequency distribution:
37 | 34 | 36 | 27 | 22 |
25 | 25 | 24 | 26 | 28 |
30 | 31 | 29 | 28 | 30 |
32 | 31 | 28 | 27 | 30 |
30 | 32 | 35 | 34 | 29 |
Solution:
Since there are so many distinct values here, we will use grouped frequency distribution. Let’s say the intervals are 20-25, 25-30, 30-35. Frequency distribution table can be made by counting the number of values lying in these intervals.
Temperature Number of Days 20-25
2
25-30
10
30-35
13
This is the grouped frequency distribution table. It can be converted into cumulative frequency distribution by adding the previous values.
Temperature Number of Days Less than 25
2
Less than 30
12
Less than 35
25
Example 5: Make a Frequency Distribution Table as well as the curve for the data:
{45, 22, 37, 18, 56, 33, 42, 29, 51, 27, 39, 14, 61, 19, 44, 25, 58, 36, 48, 30, 53, 41, 28, 35, 47, 21, 32, 49, 16, 52, 26, 38, 57, 31, 59, 20, 43, 24, 55, 17, 50, 23, 34, 60, 46, 13, 40, 54, 15, 62}
Solution:
To create the frequency distribution table for given data, let’s arrange the data in ascending order as follows:
{13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62}
Now, we can count the observations for intervals: 10-20, 20-30, 30-40, 40-50, 50-60 and 60-70.
Interval Frequency 10 – 20 7 20 – 30 10 30 – 40 10 40 – 50 10 50 – 60 10 60 – 70 3 From this data, we can plot the Frequency Distribution Curve as follows:
Read More:
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