8. Find the mean and variance for the following frequency distributions.
Classes | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
Frequencies | 5 | 8 | 15 | 16 | 6 |
Classes |
Frequency
|
Mid-point
|
||||
0-10 | 5 | 5 | 25 | -22 | 484 | 2420 |
10-20 | 8 | 15 | 120 | -12 | 144 | 1152 |
20-30 | 15 | 25 | 375 | -2 | 4 | 60 |
30-40 | 16 | 35 | 560 | 8 | 64 | 1024 |
40-50 | 6 | 45 | 270 | 18 | 324 | 1944 |
= N = 50 |
= 1350 |
=6600 |
We know, Variance,
Hence, Mean = 27 and Variance = 132