1. STATISTICAL ANALYSIS Created by The North Carolina School of Science and Math.The North Carolina School of Science and Math Copyright 2012. North Carolina Department of Public Instruction.North Carolina Department of Public Instruction

2. Statistical Analysis What is it and why do we use it?  It is the use of mathematics on collected data to control manufacturing processes that aim to maximize productivity, maximize material utilization, and minimize defects, rejects, and waste.

3. Mean  MEAN ( X )  A value that is obtained by adding the terms and then dividing their sum by the number of terms  Example: 4 + 4 + 5 + 7 + 10 = 30 30 5 = 6 Mean = 6

4. Range  RANGE  The difference between the lowest and highest values in a data set  Example: 4 6 5 7 10 Range = 6

5. Median  MEDIAN  Once rank ordered (smallest to largest) it is the number in the middle  Example: 4 4 5 7 10 Median = 5

6. Standard Deviation and Variance  STANDARD DEVIATION  A measure of the variation of the data from the mean  Must calculate the Variance first  The VARIANCE can be computed as follows: Subtract the mean from each term in the distribution to obtain a set of differences Square each difference and add the squares Divide the sum of the squared differences by the number of terms in the distribution less one

7. Variance  VARIANCE  In any distribution (set of data) the data collected may vary widely or they may be very close to each other.  It is the mean of the squared differences from the mean of the distribution

8. Standard Deviation Taking the square root of the variance results in the standard deviation  (4-6) 2 + (4-6) 2 + (5-6) 2 + (7-6) 2 + (10-6) 2 5 - 1 S = = 2.55