1. Forging new generations of engineers

2. Introductionto Basic Statistics

3. Lesson Concepts Addressed Statistical analysis of measurements can help to verify the quality of a design or process. Engineers use graphics to communicate patterns in recorded data.

4. Related Performance Objectives Generate a data set of linear measurement. Calculate the mean, mode, median, and range of a data set. Create a histogram of recorded measurements showing class interval and frequency. It is expected that students will…

5. S xS x n x = Mean (pronounced “X-bar”) mean The mean is the sum of the values of a set of data divided by the number of values in that data set.

6. x = individual data value n = # of data values in the data set S = summation of a set of values S xS x n x = Mean

7. 3 7 12 17 21 21 23 27 32 36 44 Data Set: Sum of the values = 243 Number of values = 11 Mean = 243 11 = 22.09 S xS x n x = = Mean

8. mode The most frequently occurring value in a set of data is the mode. Symbol… M Mode 27 17 12 7 21 44 23 3 36 32 21 Data Set:

9. 3 7 12 17 21 21 23 27 32 36 44 Data Set: Mode = 21 mode The most frequently occurring value in a set of data is the mode. Mode

10. Note:If two numbers of equal frequency stand out, then the data set is “bimodal.” If more than two numbers of equal frequency stand out, then the data set is “multi-modal.” mode The most frequently occurring value in a set of data is the mode. Mode

11. median The median is the value that occurs in the middle of a set of data that has been arranged in chronological order. Symbol… x pronounced “X-tilde” ~ Median

12. Data Set: Median = 21 Median median The median is the value that occurs in the middle of a set of data that has been arranged in chronological order. 27 17 12 7 21 44 23 3 36 32 21

13. Note:A data set that contains an odd # of values always has a Median. For an even # of values, the two middle values are averaged with the result being the Median. Median 3 7 12 17 21 21 23 27 32 36 44 Data Set: Median = 21

14. range The range is the difference between the largest and smallest values that occur in a set of data. Range = 44-3 = 41 Symbol… R Range 3 7 12 17 21 21 23 27 32 36 44 Data Set:

15. A histogram is a common data distribution graph that is used to show the frequency with which specific values, or values within ranges, occur in a set of data. An engineer might use a histogram to show the most common, or average, dimension that exists among a group of identical manufactured parts. Histogram

16. 0123456-2-3-4-5-6 0 3 3 2 1 2 -3 0 1 0 1 -2 1 2 -4 1 0 -2 0 0

17. Specific values, called data elements, are plotted along the X-axis of the graph. Histogram 0123456-2-3-4-5-6 Data Elements

18. Large sets of data are often divided into limited number of groups. These groups are called class intervals. Histogram -5 to 5 Class Intervals 6 to 16-6 to -16

19. The number of data elements is shown by the frequency, which occurs along the Y- axis of the graph. Histogram Frequency 1 3 5 7 -5 to 5 6 to 16-6 to -16

20. “Is the data normal?” Translation…does the greatest frequency of the data values occur about the mean value? Normal Distribution

21. Frequency Data Elements 0123456-2-3-4-5-6 Mean Value Normal Distribution

22. “Is the process normal?” Further Translation…does the data form a bell shape curve when plotted on a histogram? Normal Distribution

23. Frequency Data Elements 0123456-2-3-4-5-6 Normal Distribution