Mean of Grouped Data
Mean of Grouped Data
Mean Of Grouped Data:
Grouped data is data that has been grouped together in categories. Mean of a set of observations is the average of the given observations. To find the mean, we divide the sum of the observations by the total number of observations. However, for grouped data, we cannot find the exact Mean, we can only give estimates.
There are three methods for finding the mean from a grouped frequency table.
1. Mean Using Class Mark.
2. Assumed Mean Method
3. Step Deviation Method
Mean of Grouped Data Using Class Mark:
The mean (or average) of observations, as we know , is the sum of the values of all the observations divided by the total number of observations. For grouped data we will find the class mark for each class and denote it with for the respective class with frequencies
, In other way we say that the frequency denotes the number times the class mark is occurring. That is why the mean calculated using grouping is not accurate but is an estimate.
Now, the sum of the values of all the observations
and the number of observations
So, the mean of the data is given by
Illustration: Find the mean of the following data:
| Class interval | 10-25 | 25-40 | 40-55 | 55-70 | 70-85 | 85-100 |
| Number of students | 2 | 3 | 7 | 6 | 6 | 6 |
Solution
| Class interval | Number of students |
Class mark |
|
|
10-25 25-40 40-55 55-70 70-85 85-100 |
2 3 7 6 6 6 |
17.5 32.5 47.5 62.5 77.5 92.5 |
35.0 97.5 332.5 375.0 465.0 555.0 |
| Total |
Find the mean of the following distribution.
| |||||||||||||||
| Right Option : C | |||||||||||||||
| View Explanation | |||||||||||||||
The arithmetic mean for the following frequency distribution is_________________.
| ||||||||||||
| Right Option : A | ||||||||||||
| View Explanation | ||||||||||||
While computing the mean of grouped data, we assume that the frequencies are ________________________. | |||
| Right Option : B | |||
| View Explanation | |||
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