Answer:
i. Mean = 11.2
ii. Variance = 14.17
iii. Standard deviation = 3.76
Step-by-step explanation:
i. Mean, m = [tex]\frac{sum of the values}{number of the values}[/tex]
= [tex]\frac{4+11+12+12+13+15}{6}[/tex]
= [tex]\frac{67}{6}[/tex]
= 11.2
The mean of the given data is 11.2
ii. Variance = [tex]\frac{sum(x_{i} - m)^{2}}{n-1}[/tex]
where: [tex]x_{i}[/tex] is the value of the one observation, m is the sample mean and n is the number of data given.
= [tex]\frac{[(4-11.2)^{2}+(11-11.2)^{2} + (12-11.2)^{2} + (12-11.2)^{2} + (13-11.2)^{2} + (15-11.2)^{2}] }{6-1}[/tex]
= [tex]\frac{[51.84+0.04+0.64+0.64+3.24+14.44]}{5}[/tex]
= [tex]\frac{70.84}{5}[/tex]
= 14.168
Variance = 14.17
iii. Standard deviation = [tex]\sqrt{Variance}[/tex]
= [tex]\sqrt{14.17}[/tex]
= 3.76
