1. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics

2. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Introduction to
Basic Statistics

3. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
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. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Related Performance Objectives
It is expected that students will…
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.

5. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Mean
The mean is the sum of the values of a set of data divided by the number of values in that data set.
S x n x =
(pronounced “X-bar”)

6. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Mean
S x x = n
x = individual data value
n = # of data values in the data set
S = summation of a set of values

7. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Mean
Data Set:
Sum of the values = 243
Number of values = 11
S x
243
Mean = x = = = n 11

8. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Mode
The most frequently occurring value in a set of data is the mode.
Symbol… M
Data Set:

9. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Mode
The most frequently occurring value in a set of data is the mode.
Data Set:
Mode = 21

10. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Mode
The most frequently occurring value in a set of data is the mode.
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.”

11. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Median
The median is the value that occurs in the middle of a set of data that has been arranged in numerical order. ~
Symbol… x pronounced “X-tilde”

12. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Median
The median is the value that occurs in the middle of a set of data that has been arranged in numerical order.
Data Set:
Median = 21

13. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Median
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.
Data Set:
Median = 21

14. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Range
The range is the difference between the largest and smallest values that occur in a set of data.
Symbol… R
Data Set:
Range = = 41

15. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Histogram
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.

16. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics 3 -1 -3 3 2 1 -1 -1 2 1 1 -1 -2 1 2 1 -2 -4 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

17. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Histogram
Specific values, called data elements, are plotted along the X-axis of the graph. -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
Data Elements

18. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Histogram
Large sets of data are often divided into limited number of groups. These groups are called class intervals.
-6 to -16
-5 to 5
6 to 16
Class Intervals

19. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Histogram
The number of data elements is shown by the frequency, which occurs along the Y-axis of the graph. 7 5
Frequency 3 1
-16 to -6
-5 to 5
6 to 16

20. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Normal Distribution
“Is the data normal?”
Translation…does the greatest frequency of the data values occur about the mean value?

21. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Normal Distribution
Mean Value
Frequency -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
Data Elements

22. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Normal Distribution
“Is the process normal?”
Further Translation…does the data form a bell shape curve when plotted on a histogram?

23. Introduction to Basic Statistics
Introduction to Engineering Design TM
Unit 1 – Lesson 1.3 – Measurement and Statistics
Normal Distribution
Frequency -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
Data Elements