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

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population mean and standard deviation

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

Jul 21, 2023 203 likes •330 views

Population Mean and Standard Deviation In a population with N members Population mean: = x 1 + x 2 + . . . + x N N Population standard deviation: ( x 1 ) 2 + ( x 2 ) 2 + . . . + ( x N ) 2 = N MA202 Sections 5

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SLIDE 1

Population Mean and Standard Deviation

In a population with N members Population mean: µ = x1 + x2 + . . . + xN N Population standard deviation: σ =

(µ − x1)2 + (µ − x2)2 + . . . + (µ − xN)2

N

MA202 Sections 5 & 401 Chapter 9-3 Graphs

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SLIDE 2

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 80 = 64.2 σ =

(64.2 − 64)2 + (64.2 − 63)2 + . . . + (64.2 − 63)2

80 = 1.9

MA202 Sections 5 & 401 Chapter 9-3 Graphs

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SLIDE 3

Sample Mean and Standard Deviation

In a sample with n members Sample mean: x = x1 + x2 + . . . + xn n Sample standard deviation: s =

(x − x1)2 + (x − x2)2 + . . . + (x − xn)2

n

MA202 Sections 5 & 401 Chapter 9-3 Graphs

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SLIDE 4

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 To choose our sample: 66 64 62 64 66 64 62 64 66 63 x = 66 + 64 + 62 + 64 + 66 + 64 + 62 + 64 + 66 + 63 10 = 64.1 s =

(64.1 − 66)2 + (64.1 − 64)2 + . . . + (64.1 − 63)2

10 = 1.45

MA202 Sections 5 & 401 Chapter 9-3 Graphs

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SLIDE 5

Relative Frequency

MA202 Sections 5 & 401 Chapter 9-3 Graphs

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SLIDE 6

Relative Frequency

MA202 Sections 5 & 401 Chapter 9-3 Graphs

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SLIDE 7

Relative Frequency vs Normal Distribution

MA202 Sections 5 & 401 Chapter 9-3 Graphs

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SLIDE 8

The 68-95-99.7 Rule for Normal Distributions

MA202 Sections 5 & 401 Chapter 9-3 Graphs

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SLIDE 9

Standardizing the Normal Distribution

MA202 Sections 5 & 401 Chapter 9-3 Graphs

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SLIDE 10

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

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SLIDE 11

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

f 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

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SLIDE 12

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