Question

#2

Consider the followi ng sample of 44 observations: 8.9: 12.4: 8.6: 11.3; 9.2; 8.8;8.8; 6.2; .07; 7.1; 8; 10.7; 7.6; 9.1; 9.2; 8.2; 9.0; 8.7; 9.1; 10.9;10.3; 9.6; 7.8; 11.5; 9.3; 7.9; 8.8; 12.7; 8.4; 7.8; 5.7; 10.5; 10.5; 9.6; 8.9;10.2; 10.3; 7.7; 10.6; 8.3; 8.8; 9.5; 8.8; 9.4. 1. Find the mean and the standard deviation for the data given.

Answer 1

1).

$\bar x =\frac{\sum x}{n}$

$\bar x =\frac{398.57}{44} = 9.0584$

$s =\sqrt{ \frac{\sum x^2- (\sum x)^2 /n)}{n-1}}$

$s =\sqrt{ \frac{3786.3749 - ( 398.57)^2 /44}{44-1}} = 2.0229$

2).

empirical rule
mean - 1s	7.0355
mean + 1s	11.0813
percent in interval (68.26%)	81.8%
mean - 2s	5.0126
mean + 2s	13.1042
percent in interval (95.44%)	97.7%
mean - 3s	2.9896
mean + 3s	15.1272
percent in interval (99.73%)	97.7%