Question

Your teacher will show you how to use a calculator to find the mean and standard deviation for the following set of data. A set of eight men have heights (in inches)

as shown below.
67.0 70.9 67.6 69.8 69.7 70.9 68.7 67.2
Indicate the mean and standard deviation you obtained from your calculator to the nearest hundredth.

Answer 1

Answer: Mean = 68.98 inches and Standard deviation = 1.59 inches

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 :-

`\overline{x}=(\sum^n_(i=1)x_i)/(n)`

`\\\\\Rightarrow\ \overline{x}=(67.0 +70.9+ 67.6+ 69.8+ 69.7 +70.9 +68.7+ 67.2)/(8)\\\\=(551.8)/(8)=68.975\approx68.98` (Using calculator)

The formula to find the standard deviation is given by :-

`\sigma(X)=\sqrt{\frac{\sum_(i=1)^n(x_i-\overline{x})^2}{n-1}}`

Now,

`\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`

`=3.900625+3.705625+1.890625+0.680625+0.525625+3.705625+0.075625+3.150625\\\\=17.635`

Now, standard deviation of the above results will be :-

`\sigma(x)=\sqrt{(17.635)/(8-1)}\\\\=\sqrt{(17.635)/(7)}\\\\=1.58722579184\approx1.59` (Using calculator)

Hence, the standard deviation of these results = 1.59