How can one estimate the mean and variance of data that are summarized in a grou
ID: 3750262 • Letter: H
Question
How can one estimate the mean and variance of data that are summarized in a grouped frequency distribution? Please use excel
California Census Data Under 5 years 5 to 9 years 10 to 14 years 15 to 19 years 20 to 24 years 25 to 34 years 35 to 44 years 45 to 54 years 55 to 59 years 60 to 64 years 65 to 74 years 75 to 84 years 85 years and over Number Percent 2,486,981 2,725,880 2,570,822 2,450,888 2,381,288 5,229,062 5,485,341 16.2% 4,331,635 12.8% 1,467,252 1,146,841 1,887,823 1,282,178 80% 2010 7.0% 15.4% 4.3% 3.4% 55% 38% 425,657 1.3%Explanation / Answer
frequency Min Max mid point frequency*midpoint frequency*midpoint*midpoint 2486981 0 4 2 4973962 9947924 2725880 5 9 7 19081160 133568120 2570822 10 14 12 30849864 370198368 2450888 15 19 17 41665096 708306632 2381288 20 24 22 52388336 1152543392 5229062 25 34 29.5 154257329 4550591205.5 5485341 35 44 39.5 216670969.5 8558503295.25 4331635 45 54 49.5 214415932.5 10613588658.75 1467252 55 59 57 83633364 4767101748 1146841 60 64 62 71104142 4408456804 1887823 65 74 69.5 131203698.5 9118657045.75 1282178 75 84 79.5 101933151 8103685504.5 425657 85 94 89.5 38096301.5 3409618984.25 Sum of frequency 33871648 Sum= Sum of corresponding column 1160273306 55904767682 Mean= (Sum of freq*midPoint/Sum of freq) 34.255000111 Variance= (sumof freq*midPoint*midPoint/Sum of freq – Mean*Mean) 477.0835318131
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