1. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Materials and Processes Statistical Process Control (SPC) 5.6 calculate the mean and standard deviation of a sample or population

2. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Performance Objective Given a data set of a sample or population calculate the mean and standard deviation using an electronic spread sheet.

3. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Enabling Objectives 1.match the following terms with the appropriate definition: statistical process control (SPC), mean, standard deviation (sigma), population, sample, normal distribution (bell curve), tolerance, upper and lower limits 2.calculate a mean 3.calculate a standard deviation

4. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Quality Control Classical Quality Control is achieved by observing (measuring & testing) important properties of the finished product to determine acceptance or rejection. Statistical Process Control uses statistical tools to observe the performance of the production line to predict significant deviations that may result in rejected products.

5. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Normal Distribution At the heart of statistical process control is the concept of a normal distribution or bell- shaped curve. The frequency distribution of many events in nature and in processes used in manufacturing are found in practice to be approximated closely by the normal curve, and they are said to be normally distributed.

6. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Bell-shape Curve The frequency curve, which is bell-shaped, is called the normal curve or normal distribution.

7. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Statistical Process Control (SPC) Statistical Process Control is a method for achieving quality control in manufacturing processes using statistical tools to detect if production is within limits. Two of the more common tools used are mean and standard deviation which also describe the shape of the normal distribution.

8. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Sample & Population Often the size of a group makes it impractical to perform SPC calculations of the population. When this occurs, a sample is used. The population is the entire group. A sample is a sub-group of the population with the expectation that it is representative of the larger group.

9. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Mean Mean is the average of a set of scores or values and is represented by the symbol,. The mean is calculated by adding the set of values then dividing by the number of values. Example:

10. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Mean height of female high school students in the USA It would be very impractical to measure the height of all female high school students in the USA in order to calculate their mean height. It would be more practical to use a sample and only measure the height of the female students in your high school.

11. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Standard Deviation Standard Deviation is an estimate of the average each item’s value differs from the group’s mean. Standard deviation is represented by the symbol,.

12. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Standard Deviation of a Population The formula for calculating the standard deviation of a population is: Although this formula may appear complicated, it is relatively easy to solve.

13. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Example—population data: 5, 2, 8, 6, 4 Step 1: List the values of the data in the first column of the table labeled x. Step 2: Calculate the mean of the data in the first column. x 5 2 8 6 4 = 5

14. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Example—population data: 5, 2, 8, 6, 4 Step 3: Complete column two by subtracting the mean from each item value,. x 50 2-3 83 61 4 = 5

15. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Example—population data: 5, 2, 8, 6, 4 Step 4: Now square the value in column two and enter it in column three. Step 5: Sum the values in column three and divide by n. 20/5 = 4 x 500 2-39 839 611 41 = 5 = 20

16. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Example—population data: 5, 2, 8, 6, 4 Step 6: To obtain the standard deviation of the data, finish by calculating the square root of the value obtained in step 5.

17. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Standard Deviation of a Sample The formula for calculating the standard deviation of a sample is: The only difference between the two standard deviation formulas is the denominator (n vs. n – 1).

18. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Test Your Understanding Without performing calculations on paper, what is the mean of the following population of data: 20, 40, 50, 60, 80? A.5 B.20 C.50 D.60 Hint: Mean is the average

19. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Test Your Understanding Without performing calculations on paper, what is the standard deviation of the following population of data: 20, 40, 50, 60, 80? A.5 B.20 C.50 D.60 Hint: Standard deviation is the estimated average each item deviates from the mean

20. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Electronic Spreadsheet Microsoft Excel is an excellent tool to calculate both the mean and standard deviation of a population or sample. The command AVERAGE would be used to calculate the mean. The command STDEVP would be used to calculate the standard deviation of a population. The command STDEV would be used to calculate the standard deviation of a sample.

21. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Excel Spreadsheet The graphic to the right shows the use of a spreadsheet to calculate the mean and standard deviation of a sample.

22. Developed at Utah State University Dept of Engr & Tech Educ — www.ete.usu.edu Materials and Processes 5.6 calculate the mean and standard deviation of a sample or population Happy Calculating