the mean of ungrouped data and the mean calculated when the same data is grouped are always the same do you agree with this statement give reason for the answer
Answers
Mean is always same if grouping is Done according to existing value and may not be same if grouped for a range
Step-by-step explanation:
the mean of ungrouped data and the mean calculated when the same data is grouped are always the same if grouping is Done for all existing values
Example
Ungrouped data 1 , 1 , 2 , 3 , 3 , 3 , 4 , 5 , 5 , 6
Total Data = 10 Sum = 33 Mean = 3.3
Grouped data -
1 2 2
2 1 2
3 3 9
4 1 4
5 2 10
6 1 6
10 33
Mean = 3.3
the mean of ungrouped data and the mean calculated when the same data is grouped are not always the same if grouping is Done for range
Now if same data is grouped in range
1 - 3 2 6 12
4 - 6 5 4 20
10 32
Mean = 32/10 = 3.2 ≠ 3.3
Now if i change data 1 , 1 , 2 , 2 , 3 , 3 , 4 , 5 , 5 , 6
Mean = 3.2
1 - 3 2 6 12
4 - 6 5 4 20
10 32
Mean = 32/10 = 3.2 = 3.2
Here Mean can be same or not
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Answer:
the mean of ungrouped data observation are taken by actual observation
where as while calculating grouped data the observation is the class mark.
Therefore the mean will not be same.