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.
1427 1228 987
699 725 830
726 748 544
627 1441 950
(a) find the sample mean.
\\( \overline { x } = \\) (round to one decimal place as needed.)

Explanation:

Step1: Sum all the data points

$$1427 + 1228+987 + 699+725+830+726+748+544+627+1441+950$$
$$=(1427+1228)+(987 + 699)+(725+830)+(726+748)+(544+627)+(1441+950)$$
$$=2655+1686+1555+1474+1171+2391$$
$$=(2655+1686)+(1555+1474)+(1171+2391)$$
$$=4341+3029+3562$$
$$=4341+(3029+3562)$$
$$=4341 + 6591=10932$$

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 \(\sum_{i=1}^{n}x_{i}=10932\)
\(\bar{x}=\frac{10932}{12}=911.0\)

Answer:

\(911.0\)