Question

Auto pistons at Wemming​ Chung's plant in Shanghai are produced in a forging​ process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each​ day, the mean and the range of this diameter have been as​ follows:

Day Mean Bold x overbar ​(mm) Range R ​(mm)
1 158.9 4.0
2 151.2 4.6
3 155.6 4.3
4 155.5 5.0
5 154.6 4.3

a) What is the value of x ?

Answer 1

Missing part of the question

b)What is the value of R?

Answer:

a. X = 155.2

b. R = 4.4

Explanation:

a. Calculating the value of x.

The value of x is the mean of the mean observation; i.e. the mean column

Mean is calculated as: the summation of all observation divided by the number of observations.

Summation of Observation = 158.9 + 151.2 + 155.6 + 155.5 + 154.6

Summation of Observation = 775.8

Number of Observations = 5

X = Mean = 775.8/5

X = 155.16

X = 155.2 ----- Approximated to 1 decimal place

b. Calculating the value of R.

The value of R is the mean/average of the Range

Mean is calculated as: the summation of all observation divided by the number of observations.

Summation of Observation = 4.0 + 4.6 + 4.3 + 5.0 + 4.3

Summation of Observation = 22.2

Number of Observations = 5

R = Mean = 22.2/5

R = 4.44

R = 4.4 ----- Approximated to 1 decimal place