Question

the empirical rule for 20 gas stations ranging from $2.45 to $2.57 how do you find the mean, variance, deviation, standard deviation, and the empirical rule (gas prices 2.45, 2.46, 2.46,2.46,2.46,2.47,2.47,2.48,2.48,2.48,2.55,2.55,2.56,2.56,2.56,2.56,2.57,2.57,2.57,2.57)

Answer 1

Following table shows the calculations

	Gas Price, x	(x-mean)^2
	2.45	0.00416025
	2.46	0.00297025
	2.46	0.00297025
	2.46	0.00297025
	2.46	0.00297025
	2.47	0.00198025
	2.47	0.00198025
	2.48	0.00119025
	2.48	0.00119025
	2.48	0.00119025
	2.55	0.00126025
	2.55	0.00126025
	2.56	0.00207025
	2.56	0.00207025
	2.56	0.00207025
	2.56	0.00207025
	2.57	0.00308025
	2.57	0.00308025
	2.57	0.00308025
	2.57	0.00308025
Total	50.29	0.046695

Now sample size: n=20

The sample mean:

The variance is:

The standard deviation is:

Empirical rule:

68% data values lie in the interval:

95% data values lie in the interval:

99.7% data values lie in the interval: