The distances in meters for seven throws of a shotputter are: $14.5,15.2,16.8,17.1,15.9,16.3,14.7$. Calculate the sample mean and sample standard deviation. Round to two decimals.

Given observations are:

$14.5,15.2,16.8,17.1,15.9,16.3,14.7$

Number of observations:

$n=7$

Sample mean is

$\bar{x}=\frac{14.5+15.2+16.8+17.1+15.9+16.3+14.7}{7}$

$\bar{x}=\frac{110.5}{7}$

$\bar{x}=15.7857$

So,

$\bar{x}\approx 15.79$

Now, sample standard deviation is

$s=\sqrt{\frac{\sum (x_i-\bar{x})^2}{n-1}}$

Here,

$\sum (x_i-\bar{x})^2\approx 6.2086$

So,

$s=\sqrt{\frac{6.2086}{6}}$

$s=\sqrt{1.0348}$

$s\approx 1.0172$

So,

$s\approx 1.02$

Therefore, the sample mean and sample standard deviation are $15.79,\ 1.02$.