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

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

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.

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.

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”)

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

Introduction to Basic Statistics Introduction to Engineering Design TM Unit 1 – Lesson 1.3 – Measurement and Statistics Mean Data Set: 3 7 12 17 21 21 23 27 32 36 44 Sum of the values = 243 Number of values = 11 S x 243 Mean = x = = = 22.09 n 11

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: 27 17 12 7 21 44 23 3 36 32 21

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: 3 7 12 17 21 21 23 27 32 36 44 Mode = 21

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.”

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”

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: 27 17 12 7 21 44 23 3 36 32 21 Median = 21

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: 3 7 12 17 21 21 23 27 32 36 44 Median = 21

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: 3 7 12 17 21 21 23 27 32 36 44 Range = 44-3 = 41

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.

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

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

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

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

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?

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

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?

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