Question

Calculate mean, variance and standard deviation for the following distribution. | Classes | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 | |---------|-------|-------|-------|-------|-------|-------|--------| | Frequency | 3 | 7 | 12 | 15 | 8 | 3 | 2 |

Find the mean and standard deviation using short-cut method. | xi | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | |----|----|----|----|----|----|----|----|----|----| | fi | 2 | 1 | 12 | 29 | 25 | 12 | 10 | 4 | 5 |