Question

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. 2.4 3.1 2.9 1.6 0.9 4.0 2.3 1.2 3.5 0.3 2.1 3.4 (a) find the sample mean. \\( \bar { x } = \square \\) (round to two decimal places as needed)

Explanation:

Step1: Sum all the data points

$$\begin{align*} &2.4 + 3.1+2.9 + 1.6+0.9 + 4.0+2.3+1.2+3.5+0.3+2.1+3.4\\ =&(2.4 + 3.1)+(2.9 + 1.6)+(0.9 + 4.0)+(2.3 + 1.2)+(3.5 + 0.3)+(2.1 + 3.4)\\ =&5.5+4.5+4.9+3.5+3.8+5.5\\ =&(5.5+4.5)+(4.9+3.5)+(3.8+5.5)\\ =&10+8.4+9.3\\ =&27.7 \end{align*}$$

Step2: Calculate the sample mean

The formula for the sample mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 12\) (the number of data - points) and \(\sum_{i=1}^{n}x_{i}=27.7\)
\(\bar{x}=\frac{27.7}{12}\approx2.31\)

Answer:

\(2.31\)