The grade point averages (GPA) for 12 randomly selected college students are shown on the right. Complete parts (a) through (c) below.
Assume the population is normally distributed.
$\begin{array}{lll}2.3 & 3.3 & 2.8 \\ 1.6 & 0.9 & 4.0 \\ 2.5 & 1.4 & 3.8 \\ 0.3 & 2.3 & 3.1\end{array}$
(a) Find the sample mean.
$\bar{x}=2.36$ (Round to two decimal places as needed.)
(b) Find the sample standard deviation.
$s=\square$ (Round to two decimal places as needed.)
Answer
Rounding to two decimal places, the final answer is: \(\boxed{1.14}\)
Step 1 ：The given data is: \(2.3, 3.3, 2.8, 1.6, 0.9, 4.0, 2.5, 1.4, 3.8, 0.3, 2.3, 3.1\)
Step 2 ：The sample mean \(\bar{x}\) is calculated as \(2.36\)
Step 3 ：To find the sample standard deviation, we first need to calculate the variance. The variance is the average of the squared differences from the mean.
Step 4 ：After calculating the variance, we take the square root to get the standard deviation.
Step 5 ：The calculated standard deviation is approximately \(1.1397434586410888\)
Step 6 ：Rounding to two decimal places, the final answer is: \(\boxed{1.14}\)
