Math Assignment Help With Variance Of Grouped Data
10.3.3 Variance of grouped data:
Step Deviation Method: When data are grouped into a frequency distribution having class intervals of equal size h, the formula used is;
Example: Calculate the mean and standard deviation for the following distribution:
| Marks | Number of students |
|---|---|
20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90 |
3 6 13 15 14 5 4 |
Solution: firstly let’s find the mid values of the class intervals and consider a suitable assumed mean, A
Class interval |
Frequency fi |
Mid-value xi |
ui = xi – A/10 |
fi ui |
fiui2 |
|---|---|---|---|---|---|
20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90 |
3 6 13 15 14 5 4 |
25 35 45 55 65 75 85 |
-3 -2 -1 0 1 2 3 |
-9 -12 -13 0 14 10 12 |
27 24 13 0 14 20 36 |
Σ fi = 60 |
Σfi ui = 2 |
Σfiui2 = 134 |
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