Population Mean and Standard Deviation In a population with N members - PowerPoint PPT Presentation

Population Mean and Standard Deviation In a population with N members Population mean: µ = x 1 + x 2 + . . . + x N N Population standard deviation: ( µ − x 1 ) 2 + ( µ − x 2 ) 2 + . . . + ( µ − x N ) 2 � σ = N MA202 Sections 5 & 401 Chapter 9-3 Graphs

Example 9.14 64 63 65 66 67 65 64 62 65 68 68 62 63 64 64 67 67 65 64 62 59 63 61 63 66 66 61 64 64 62 63 60 63 66 64 66 64 64 67 61 64 64 62 69 65 62 63 69 63 62 65 63 65 65 65 66 65 65 63 62 63 64 64 64 65 66 65 65 63 63 66 66 63 64 66 63 63 64 65 63 µ = 64 + 63 + . . . + 63 = 64 . 2 80 � (64 . 2 − 64) 2 + (64 . 2 − 63) 2 + . . . + (64 . 2 − 63) 2 σ = = 1 . 9 80 MA202 Sections 5 & 401 Chapter 9-3 Graphs

Sample Mean and Standard Deviation In a sample with n members Sample mean: x = x 1 + x 2 + . . . + x n n Sample standard deviation: � ( x − x 1 ) 2 + ( x − x 2 ) 2 + . . . + ( x − x n ) 2 s = n MA202 Sections 5 & 401 Chapter 9-3 Graphs

Example 9.15 We generate a sequence of random numbers: 5, 5, 2, 9, 1, 0, 4, 5, 3, 1, 2, 4, 1, 6, 6, 9, 1, 7 66 64 62 64 66 To choose our sample: 64 62 64 66 63 x = 66 + 64 + 62 + 64 + 66 + 64 + 62 + 64 + 66 + 63 = 64 . 1 10 (64 . 1 − 66) 2 + (64 . 1 − 64) 2 + . . . + (64 . 1 − 63) 2 � s = = 1 . 45 10 MA202 Sections 5 & 401 Chapter 9-3 Graphs

Relative Frequency MA202 Sections 5 & 401 Chapter 9-3 Graphs

Relative Frequency MA202 Sections 5 & 401 Chapter 9-3 Graphs

Relative Frequency vs Normal Distribution MA202 Sections 5 & 401 Chapter 9-3 Graphs

The 68-95-99.7 Rule for Normal Distributions MA202 Sections 5 & 401 Chapter 9-3 Graphs

Standardizing the Normal Distribution MA202 Sections 5 & 401 Chapter 9-3 Graphs

Standardizing the Normal Distribution If we are measuring the weights of full-term newborn babies... What does a z -score of − 1 . 75 indicate? What does a z -score of 0 . 15 indicate? What does a baby in the 85th percentile indicate? MA202 Sections 5 & 401 Chapter 9-3 Graphs

Class Discussion If we want to determine where UK students live, and we choose every 250th student alphabetically. What is the population? Is the sample random? If Mitch McConnell wants voters opinions of his constituents, is a questionnaire sent to each one likely to be representative of everyone? What if he sends it to a sample of registered Republicans? If in fact, only 1 in 10 dentists recommend Whito Toothpaste, is it possible for them to advertise that 8 in 10 do? In the shoe business, which average of foot size is most important (mean, median or mode)? MA202 Sections 5 & 401 Chapter 9-3 Graphs

Homework Homework 2 (due 2/9/09): Section 9.1 # 2, 8a, 9, 16, 18, 26, 34 Section 9.2 # 1, 3, 5b-e, 9, 13, 24, 33 Section 9.3 # 2, 11, 14, 17, 18, 31 MA202 Sections 5 & 401 Chapter 9-3 Graphs