The assignment content discusses various statistical concepts such as mean, median, mode, sum of squares, variance, and standard deviation. It also includes the calculation of cumulative percentage for a given data set.
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Running head: PSYCHOLOGICAL AND INSTITUTIONAL STATISTICS PSYCHOLOGICAL AND INSTITUTIONAL STATISTICS [Document subtitle] [DATE] [Company name] [Company address]
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1 PSYCHOLOGICAL AND INSTITUTIONAL STATISTICS 1)MEAN:3+8+5+9+6+3+5+2+7+7+3=58= 5.27 1111 2)MEDIAN: Median is the middle value of the series when arranged in ascending order. The middle value in this series is- 5. Therefore Median is 5 3)MODE: Mode is the number that is most repeated in a set of population. Therefore, in the given series 3 is repeated mostly. Mode of the series is: 3 4)SUM OF SQUARES Data (x) Squareof x 24 39 39 39 525 525 636 749 749 864 981 Sum360 Data (X) 2 3 3 3 5 5 6 7 7 8 9
2 PSYCHOLOGICAL AND INSTITUTIONAL STATISTICS 5)VARIANCE Data (X)X-x, where x=mean(X-x)2 22-5.2710.6929 33-5.275.1529 33-5.275.1529 33-5.275.1529 55-5.270.0729 55-5.270.0729 66-5.270.5329 77-5.272.9929 77-5.272.9929 88-5.277.4529 99-5.2713.9129 Sum54.1819 The variance for the data is 54.1819 6)STANDARD DEVIATION: S.D. is Square Root of Variance = Square Root of 54.1819 = 7.36 Calculate the following based on the data set above as a SAMPLE 7)MEAN:3+5+6+7+8+9=38= 6.3 66 8)VARIANCE Variance is 23.3334 Data (X) X-x,where x=MeanX-x Square of ( X- x) 33-6.3-3.3311.0889 55-6.3-1.331.7689 66-6.3-0.330.1089 77-6.30.670.4489 88-6.31.672.7889 99-6.32.677.1289 Sum23.3334
3 PSYCHOLOGICAL AND INSTITUTIONAL STATISTICS 9)STANDARD DEVIATION : S.D. is Square Root of Variance = Square Root of 23.3334 = 4.83 10)For the following data set calculate the cumulative percentage for X=4 Answer Data (X) Cumulative Frequency(X/33)*100 Cumulative Percentage 44(4/33)*10012.12121212 59(9/33)*10027.27272727 514(14/33)*10042.42424242 418(18/33)*10054.54545455 321(21/33)*10063.63636364 425(25/33)*10075.75757576 126(26/33)*10078.78787879 228(28/33)*10084.84848485 432(32/33)*10096.96969697 133(33/33)*100100