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The median class in grouped data is the class interval within which the median lies. To determine this, you first calculate the cumulative frequency for each class, then find the total number of observations (N).
The median position is given by N/2. The class that contains this position is the median class.
For example, if you have a total of 50 observations, the median position is at 50/2 = 25. You then look at the cumulative frequencies of your classes until you find the first cumulative frequency that is greater than or equal to 25. The class associated with this cumulative frequency is the median class.
This method allows you to pinpoint the class interval that effectively divides the dataset into two equal parts, with half the observations below and half above this class.
1. Find the median class of the following Frequency Distribution
Class Interval | Frequency |
|---|---|
0 - 10 | 5 |
10 - 20 | 8 |
20 - 30 | 12 |
30 - 40 | 7 |
40 - 50 | 3 |
Calculate Cumulative Frequency
Class Interval | Frequency | Cumulative Frequency |
|---|---|---|
0 - 10 | 5 | 5 |
10 - 20 | 8 | 13 |
20 -30 | 12 | 25 |
30 - 40 | 7 | 32 |
40 - 50 | 3 | 35 |
Total frequency (N) = 35
Median class is the class where cumulative frequency is just greater than N / 2
N/2 = 17.5
The median class is 20 - 30.
2. Find the median class of the following Frequency Distribution
Class Interval | Frequency |
|---|---|
5-10 | 2 |
10-15 | 4 |
15-20 | 6 |
20-25 | 5 |
25-30 | 3 |
Calculate Cumulative Frequency
Class Interval | Frequency | Cumulative Frequency |
|---|---|---|
5-10 | 2 | 2 |
10-15 | 4 | 6 |
15-20 | 6 | 12 |
20-25 | 5 | 17 |
25-30 | 3 | 20 |
Total frequency (N) = 20
Median class is the class where cumulative frequency is just greater than N / 2
N/2 = 10
The median class is 15-20
3. Find the median class of the following Frequency Distribution.
Class Interval | Frequency |
|---|---|
5-10 | 3 |
10-15 | 7 |
15-20 | 9 |
20-25 | 6 |
25-30 | 5 |
Calculate Cumulative Frequency
Class Interval | Frequency | Cumulative Frequency |
|---|---|---|
5-10 | 3 | 3 |
10-15 | 7 | 10 |
15-20 | 9 | 19 |
20-25 | 6 | 25 |
25-30 | 5 | 30 |
Total frequency (N) = 30
Median class is the class where cumulative frequency is just greater than N / 2
N/2 = 15
The median class is 15-20
4. Find the median class of the following Frequency Distribution.
Class Interval | Frequency |
|---|---|
5-15 | 8 |
15-25 | 12 |
25-35 | 15 |
35-45 | 9 |
45-55 | 6 |
Calculate Cumulative Frequency
Class Interval | Frequency | Cumulative Frequency |
|---|---|---|
5-15 | 8 | 8 |
15-25 | 12 | 20 |
25-35 | 15 | 35 |
35-45 | 9 | 44 |
45-55 | 6 | 50 |
Total frequency (N) = 50
Median class is the class where cumulative frequency is just greater than N / 2
N/2 = 25
The median class is 25 -35
