Problem

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.)

Solution

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: \(\boxed{1.14}\)

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Source: https://solvelyapp.com/problems/19032/

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