Question

A bearing manufacturer wants to determine the inner diameter of a certain grade of bearing. Ideally, the diameter would be 15 mm. The data are given in table 2

TIRE NUMBER	B1	B2	B3	B4	B5	B6	B7	B8
DIAMETER	14.70	15.10	14.90	14.80	14.89	14.95	14.93	15.05

A. Find the sample mean and median.

b. Find the sample variance, standard deviation.

c. Analyze the shape of sample data using skewness and kurtosis.

Answer 1

The provided data is,

TIRE NUMBER	B1	B2	B3	B4	B5	B6	B7	B8
DIAMETER	14.7	15.1	14.9	14.8	14.89	14.95	14.93	15.05

Here, sample size (n) = 8

Let X be the inner diameter of a certain grade of bearing.

(A).

Mean:

The sample mean is,

Therefore, the sample mean is 14.915.

Median:

Arrange the given data in a sorted order as shown below

14.7

14.8

14.89

14.9

14.93

14.95

15.05

15.1

The median is calculated by taking the average of observations 14.9 and 14.93 that lies at the position 4th and position 5th position respectively starting from the left hand side of the data.

Median = (14.9 + 14.93)/2 = 29.83/2 =14.915

Therefore, the median is 14.915.

(d).

The sample variance (s) is given by,

Therefore, the sample variance is 0.0163.

The sample standard deviation (s) is given by,

Therefore, the sample standard deviation is 0.1277.

(C).

The skewness can be calculated as,

The formula to calculate kurtosis is,

---(1)

First calculate the numerator value of (1),

Substitute the value in (1), we get kurtosis

Since, the value of both skewness and kurtosis is 0, so it can be said that the shape of the sample data is mesokurtic; that is, normal curve.