Fundamentals of Statistics Dale H. Besterfield.pptx

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1. Fundamentals of Statistics

2. Collection of Data Variables: Those quality characteristics that are measurable, such as a weight measured in grams. Attributes: Those quality characteristics that are classified as either conforming or not conforming to specifications, such as a “go/no go gage.”

3. Collection of Data Continuous Variable: A variable that is capable of any degree of subdivision is referred to as continuous . Example: The weight of a gray iron casting, which can be measured as 11 kg, 11.33 kg, or 11.3398 kg, depending on the accuracy of the measuring instrument, is an example of a continuous variable. Discrete Variable : Variables that exhibit gaps are called discrete . Example: The number of nonconforming rivets in a travel trailer can be any whole number, such as 0, 3, 5, 10, 96, . . . ; however, there cannot be, say, 4.65 nonconforming rivets in a particular trailer.

4. Applications The histogram describes the variation in the process. It is used to 1. Solve problems. 2. Determine the process capability. 3. Compare with specifications. 4. Suggest the shape of the population. 5. Indicate discrepancies in data such as gaps.

5. Median Median is the value which divides a series of ordered observations so that the number of items above it is equal to number below it.

6. Example 1 The mean value of the weight of a particular brand of cereal for the past year is 0.297 kg with a standard deviation of 0.024 kg. Assuming normal distribution, find the percent of the data that falls below the lower specification limit of 0.274 g.

7. Example 2 The mean value of the weight of a particular brand of cereal for the past year is 0.297 kg (10.5 oz ) with a standard deviation of 0.024 kg. Assuming normal distribution, determine the percentage of the data that fall above 0.347 kg. 42 42

8. Example 3 A large number of tests of line voltage to home residences show a mean of 118.5 V and a population standard deviation of 1.20 V. Determine the percentage of data between 116 and 120 V.

9. Example 3 (Contd.)

10. Example 4 (contd.) If it is desired to have 12.1% of the line voltage below 115 V, how should the mean voltage be adjusted? The dispersion is σ = 1.20 V.

11. Example 4