Class Frequency X m X m 2 f X m 2 f X m 0 990025 118803 1194 200 399

Class frequency x m x m 2 f x m 2 f x m 0 990025

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Class Frequency X m X m 2 f · X m 2 f· X m 0-199 12 99.5 9900.25 118803 1194 200-399 12 299.5 89700.25 1076403 3594 400-599 7 499.5 249500.25 1746502 3496.5 600-799 1 699.5 489300.25 489300.3 699.5 800-999 1 899.5 809100.25 809100.3 899.5 1000-1199 4 1099.5 1208900.25 4835601 4398 1200-1399 1 1299.5 1688700.25 1688700 1299.5 1400-1599 2 1499.5 2248500.25 4497001 2999 Total 40 6396 6793602 15261410 18580
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S = n ( ∑ f· X m 2 ) −( ∑f· X m ) 2 n ( n 1 ) S = 40 ( 15261410 )−( 18580 ) 2 40 ( 40 1 ) = 412.342 E) Compare step ( C ) and ( D ): Although both steps were applied on the same data, we see a significant difference between them. Step C ( Original Data ) Step D ( Grouped Frequency Data ) Mean 348.9189 502 Mode/Modal Class 500 Class (0-199) and (200-399) Standard Deviation 295.9162 412.342 The main cause of this difference is because of the outliers that exist in the second data set (Frequency distribution). When it comes to the mean , we can see how the outliers really affected it in the grouped frequency data and overestimated it. The mean in step C was reasonable. The mode was more accurate in step C than step D since it was take from the original data. The standard deviation in step D is more varied than step C due to the outliers.
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F) Summary: In this phase, we calculated the five-number summary to find the theoretical upper and lower limit which guided us to find the outliers and removing them for more accuracy. Then, a box plot was constructed to show the data distribution and skewness. We also calculated the mean, median, midrange and standard deviation for the original data set (Expense). After that we found the mean, modal class and standard deviation for the same data but they were arranged in a frequency distribution table rather than dealing with each data individually, without removing the outliers. A comparison was made between step C and D and the difference was obvious due to the effect of outliers. Bibliography: Statistical Language . (2013, June 18). Retrieved May 9, 2014, from Australian Bureau of Statitics: - +what+is+a+population
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