Answer:
D. mean is 41.33, and standard deviation is 14.89
Explanation:
Given the data set: 61, 32, 33, 45, 29, 62, 22, 44, 54, 26, 28, 60 of 12 winners.
i. The mean of the data set = [tex]\frac{sum of data set}{number of data set}[/tex]
= [tex]\frac{61 + 32 + 33 + 45 + 29 + 62 + 22 + 44 + 54 + 26 + 28 + 60}{12}[/tex]
= [tex]\frac{496}{12}[/tex]
= 41.3333
The mean of the data set = 41.33
ii. Standard deviation = [tex]\sqrt{\frac{Sum(x_{i} - U) ^{2} }{N} }[/tex]
Where: [tex]x_{i}[/tex] is the value of each data set given, U is the mean, N is the number of data set.
Sum ([tex]x_{i}[/tex] - U) = [tex](61 - 41.33)^{2}[/tex] + [tex](32 - 41.33)^{2}[/tex] + [tex](33 - 41.33)^{2}[/tex] + [tex](45 - 41.33)^{2}[/tex] + [tex](29 - 41.33)^{2}[/tex] + [tex](62 - 41.33)^{2}[/tex] + [tex](22 - 41.33)^{2}[/tex] + [tex](44 - 41.33)^{2}[/tex] + [tex](54 - 41.33)^{2}[/tex] + [tex](26 - 41.33)^{2}[/tex] + [tex](28 -41.33)^{2}[/tex] + [tex](60 - 41.33)^{2}[/tex]
= 386.91 + 87.05 + 69.39 + 13.47 + 152.03 + 427.25 + 373.65 + 7.13 + 160.53 + 235.01 + 177.69 + 348.57
= 2438.68
Standard deviation = [tex]\sqrt{\frac{2438.68}{12} }[/tex]
= 14.26
Therefore, the statistics mean is 41.33 and standard deviation is 14.89
