Question

the state test scores for 12 randomly selected high school seniors are shown on the right. complete parts (a) through (c) below.
assume the population is normally distributed.
(a) find the sample mean.
\\( \overline { x } = \square \\) (round to one decimal place as needed.)

Explanation:

Step1: Sum up all the scores

$$\begin{align*} &1425 + 1228+985+692+730+830+724+747+544+621+1442+944\\ =&(1425 + 1228)+(985+692)+(730+830)+(724+747)+(544+621)+(1442+944)\\ =&2653+1677+1560+1471+1165+2386\\ =&(2653+1677)+(1560+1471)+(1165+2386)\\ =&4330+3031+3551\\ =&(4330+3031)+3551\\ =&7361+3551\\ =&10912 \end{align*}$$

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 $\sum_{i=1}^{n}x_{i}=10912$.
So, $\bar{x}=\frac{10912}{12}\approx909.3$

Answer:

$909.3$