Question

The distance (in meter) for 7 throws of a shotputter are \(14.5,15.2,16.8,17.1,15.9,16.3,14.7\). Calculate sample mean and sample standard deviation.

• A. \(14.79,\;0.88\)
• B. \(15.79,\;1.02\)
• C. \(14.79,\;1.15\)
• D. \(15.79,\;0.96\)

Hint:

For sample standard deviation always divide by \(n-1\), not by \(n\).

Answer 1

The Correct Option is D

Step 1: List the data.
The seven throws are $14.5,15.2,16.8,17.1,15.9,16.3,14.7$ metres, and $n=7$.
Step 2: Add the values.
Their sum is $14.5+15.2+16.8+17.1+15.9+16.3+14.7=110.5$.
Step 3: Compute the sample mean.
$\bar x=\dfrac{110.5}{7}\approx15.79$ metres.
Step 4: Find the squared deviations.
Subtracting $15.79$ from each value, squaring, and adding gives $\sum(x_i-\bar x)^2\approx5.49$.
Step 5: Apply the sample standard deviation formula.
Using $n-1=6$ in the denominator, $s=\sqrt{\dfrac{5.49}{6}}=\sqrt{0.915}\approx0.96$.
Step 6: State the pair.
So the mean is about $15.79$ and the sample standard deviation about $0.96$.
\[ \boxed{(15.79,\;0.96)} \]