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, 570. Find the sample mean and median.

Answer 1

The sample mean diameter of the tire is 570.5 mm, and the median diameter is 571 mm after organizing the provided data in ascending order and applying the appropriate calculations.

Step-by-step explanation:

To find the sample mean of the inner diameter of a certain grade of tire, you simply add up all the measurements and divide by the number of measurements taken. With the provided data (572, 572, 573, 568, 569, 575, 565, 570), we calculate the mean as follows:

Mean = (572 + 572 + 573 + 568 + 569 + 575 + 565 + 570) / 8 = 4564 / 8 = 570.5 mm

To find the median, which is the middle value in a list of numbers, you must first arrange the data in ascending order: 565, 568, 569, 570, 572, 572, 573, 575. Since there are 8 values, the median will be the average of the fourth and fifth values:

Median = (570 + 572) / 2 = 1142 / 2 = 571 mm

So, the sample mean diameter is 570.5 mm, and the median diameter is 571 mm.