Statistics

50

1. Convert inclusive classes to exclusive form: 9.5-19.5, 19.5-29.5, 29.5-39.5, 39.5-49.5, 49.5-59.5. 2. Range = upper limit of the highest class - lower limit of the lowest class. 3. So range = 59.5 - 9.5 = 50.

5.10

1. Total frequency n = 3+5+6+7+8 = 29. 2. The median is the 15th term, which is 30. 3. Find absolute deviations from 30: 15, 9, 3, 0, 5. 4. Multiply by frequencies: 45, 45, 18, 0, 40. 5. Sum = 148. 6. Mean deviation about median = 148/29 ≈ 5.10.

100 and 5.39

1. Total frequency n = 3+2+3+2+6+3+3 = 22. 2. Compute Σfx = 2200, so mean = 2200/22 = 100. 3. Compute variance using Σf(x-mean)²/n. 4. The weighted squared deviations sum to 640, so variance = 640/22 ≈ 29.09. 5. Standard deviation = √29.09 ≈ 5.39.

59 and 9

1. Combined mean = (50×63 + 40×54) / (50+40) = (3150 + 2160)/90 = 5310/90 = 59. 2. d1 = 63 - 59 = 4 and d2 = 54 - 59 = -5. 3. Combined standard deviation = √[(50(9²+4²) + 40(6²+5²))/90]. 4. This equals √[(50(97) + 40(61))/90] = √[(4850+2440)/90] = √81 = 9.