Respuesta :
Answer:
Mean = 189.9
Standard Deviation = 31697.093
Variance = 178.037
Population Standard Deviation = 166.538 .
Step-by-step explanation:
We are given the following data below;
X X - X bar [tex](X - Xbar)^{2}[/tex]
10.1 10.1 - 189.9 = -179.8 32328.04
45.6 45.6 - 189.9 = -144.3 20822.49
18.9 18.9 - 189.9 = -171 29241
17.9 17.9 - 189.9 = -172 29584
18.1 18.1 - 189.9 = -171.8 29515.24
15.7 15.7 - 189.9 = -174.2 30345.64
26.7 26.7 - 189.9 = -163.2 26634.24
36.9 36.9 - 189.9 = -153 23409
[tex]\sum (X-Xbar)^{2}[/tex] = 221879.65
Mean, X bar = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{10.1 +45.6+ 18.9+ 17.9+ 18.1+ 15.7+ 26.7+ 36.9}{8}[/tex]
= 189.9
Variance = [tex]\frac{\sum (X - Xbar)^{2} }{n-1}[/tex] = [tex]\frac{221879.65}{8-1}[/tex] = 31697.093
Standard deviation = [tex]\sqrt{\frac{\sum (X - Xbar)^{2} }{n-1}}[/tex] = [tex]\sqrt{31697.093}[/tex] = 178.037
Now we find that the data was actually from a population so now the formula for Population Standard deviation is given by = [tex]\sqrt{\frac{\sum (X - Xbar)^{2} }{n}}[/tex]
Population Standard Deviation = [tex]\sqrt{\frac{221879.65 }{8}}[/tex]= 166.538 .
