Statistics
ICSE · Class 11 · Mathematics
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For the ungrouped data 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, find the variance and standard deviation, and identify the correct pair.
For the discrete distribution x: 6, 10, 14, 18, 24, 28, 30 with frequencies 2, 4, 7, 12, 8, 4, 3, find the variance and standard deviation.
For the grouped data classes 4-8, 8-12, 12-16, 16-20 with frequencies 3, 6, 4, 7, find the mean and variance.
For the inclusive distribution 16-20, 21-25, 26-30, 31-35, 36-40 with frequencies 5, 6, 12, 14, 26, find the median after converting to exclusive form.
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For the grouped data 10-19, 20-29, 30-39, 40-49, 50-59 with frequencies 5, 4, 5, 3, 2, find the range after converting to exclusive form.
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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.
For the data 15, 21, 27, 30, 35 with frequencies 3, 5, 6, 7, 8, find the mean deviation about the median.
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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.
For the data 92, 93, 97, 98, 102, 104, 109 with frequencies 3, 2, 3, 2, 6, 3, 3, find the mean and standard deviation.
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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.
For the two groups with sizes 50 and 40, means 63 and 54, and standard deviations 9 and 6, find the combined mean and combined standard deviation.
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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.
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