Answer: Mean = 68.98 inches and Standard deviation = 1.59 inches
Step-by-step explanation:
Given : A set of eight men have heights (x) (in inches) as shown below.
67.0 70.9 67.6 69.8 69.7 70.9 68.7 67.2
The formula to find the mean is given by :-
[tex]\overline{x}=\dfrac{\sum^n_{i=1}x_i}{n}[/tex]
[tex]\\\\\Rightarrow\ \overline{x}=\dfrac{67.0 +70.9+ 67.6+ 69.8+ 69.7 +70.9 +68.7+ 67.2}{8}\\\\=\dfrac{551.8}{8}=68.975\approx68.98[/tex] (Using calculator)
The formula to find the standard deviation is given by :-
[tex]\sigma(X)=\sqrt{\dfrac{\sum_{i=1}^n(x_i-\overline{x})^2}{n-1}}[/tex]
Now,
[tex]\sum_{i=1}^n(x_i-\overline{x})^2=(-1.975)^2+(1.925)^2+(-1.375)^2+(0.825)^2+(0.725)^2+(1.925)^2+(-0.275)^2+(-1.775)^2[/tex]
[tex]=3.900625+3.705625+1.890625+0.680625+0.525625+3.705625+0.075625+3.150625\\\\=17.635[/tex]
Now, standard deviation of the above results will be :-
[tex]\sigma(x)=\sqrt{\dfrac{17.635}{8-1}}\\\\=\sqrt{\dfrac{17.635}{7}}\\\\=1.58722579184\approx1.59[/tex] (Using calculator)
Hence, the standard deviation of these results = 1.59
