Question

The following is a sample of sanitation scores for 20 cruise ships. 95 95 82 90 95 83 88 92 95 94 86 80 92 87 93 85 99 82 85 92

. Find the mean and standard deviation of the sanitation scores.

Calculate the intervals

x overbar plus or minus sx±s​,

x overbar plus or minus 2 sx±2s​,

x overbar plus or minus 3 sx±3s.

Answer 1

Given data is 95,95,82,90,95,83,88,92,95,94,86,80,92,87,93,85,99,82,85,92

Mean $\overline{x}=\frac{\Sigma x}{n}=\frac{1790}{20}=89.5$

$x$	95	95	82	90	95	83	88	92	95	94	86	80	92	87	93	85	99	82	85	92
$(x-\overline{x})^{2}$	$30.25$	$30.25$	$56.25$	$0.25$	$30.25$	$42.25$	$2.25$	$6.25$	$30.25$	$20.25$	$12.25$	$90.25$	$6.25$	$6.25$	$12.25$	$20.25$	$90.25$	$56.25$	$20.25$	$6.25$

Sample Variance is $\frac{\Sigma (x-\overline{x})^{2}}{n-1}=\frac{569}{20-1}=\frac{569}{19}=29.95$

and sample standard deviation is $\sqrt{29.95}=5.47$