Question

A tire manufacturer wants to determine the inner diameter of a certain grade of tire. Ideally, the diameter would be 570 mm. The data are as follows:

572, 572, 573, 568, 569, 575, 565, (a) Find the sample mean and median.

(b) Find the sample variance, standard deviation, and range.

(c) Using the calculated statistics in parts (a) and (b), can you comment on

Answer 1

Following table shows the ordered data set and calculations:

	X	(X-mean)^2
	565	31.04049796
	568	6.61209796
	569	2.46929796
	572	2.04089796
	572	2.04089796
	573	5.89809796
	575	19.61249796
Total	3994	69.71428572

(a)

Sample size n=7 Sample sum: r=3994 Sample mean: x= = =3994/7 =570.5714

Median: There are 7 data values so median will be 4th data value of ordered data set. The median is

Median = 572

(b)

Sample standard deviation: (x-7) =sqrt(69.7143/(7-1)) V n-1 =3.4087 Variance is S = -=69.7143/(7-1) n-1 =11.6191 Range Range = Maximum - Minimum =5.6 -3.9 =1.7