Central Tendency And Variability Essays Examples
There are three main measures of the central tendency: mean, mode and median (Black 76). Andrew may chose all three measures. The mode or the most frequently occurred value is the highest measure, and if he wants to get the highest mark, he should choose the mode. Katherine and Shannon may only chose between the mean and the median. The mode cannot be calculated for the Katherine’s score, and the mode for Shannon’s score has the lowest value. The median for the Katherine’s scores is 65, and the mean is (10 + 50 + 65 + 80 + 85)/5 = 58. Thus, Katherine has to choose median to have the highest score. The median of Shannon’s scores is 67, and the mean is (56 + 56 + 67 + 78 + 98)/5 = 71. Thus, Shannon have to choose the mean as the measure of the central tendency.
Mean, mode and median can be calculated using the corresponding Excel functions. For the attempt 1 mean is 37.67, median is 38, and the mode is 38. For the attempt 2, mean is 32.5, median is 28.5, and mode is 28. For the attempt 3, mean is 44.92, mode is 50 and median is 50.
As the results represent the sample from the larger population, the following formulas are used for the calculation of the variance and standard deviation (Black 79):
The calculations may be preformed in Excel using table of data of the Excel function STANDDEV. For the test 1, variance is 840.125 and standard deviation is 28.98. For the test 2, variance is 45.07 and standard deviation is 6.71. The less value of the standard deviation for the test 2 says that class 2 is less heterogeneous, and all results are closer to the sample mean value. The class 1 is more heterogeneous, as its results wary from extremely high to extremely low.
As the data reflects a sample, the formulas from the task 3 can be used. The calculations performed in Excel give the variance 52.06 and standard deviation 7.21. The standard deviation means how strongly the mean value may be different from the mean number of identified security risks. As the average number of detected risks is 37.67, the average security guard in this airport will detect 37-38 ± 7 risks or from 30 to 45 risks.
Black, Ken. Business Statistics: Contemporary Decision Making (6th ed.). New York: John Wiley & Sons. 2010. Print.