1.14 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, 570. (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 the quality of the tires?

Sample mean = 570.5

Median = 571

Range = 10

Variance = 10

Standard deviation = 3.162                                  

Step-by-step explanation:

We are given the following in the question:

572, 572, 573, 568, 569, 575, 565, 570

Sorted data: 565, 568, 569, 570, 572, 572, 573, 575

a) Sample mean

Formula:

b) Range = Maximum - Minimum = 575 - 565 = 10

Formula:

where are data points, is the mean and n is the number of observations.

Sum of squares of differences = 70

c) The mean diameter is approximately same as the ideal diameter. The diameter lies within 3.162 mm of the mean diameter. Thus, the quality of tires is good.

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step-by-step explanation: