2.1 Part 1 - Frequency Distributions

Chapter 2 Descriptive Statistics Larson/Farber 4th ed.

Section 2.1 Frequency Distributions and Their Graphs Part 1: Frequency Distributions Larson/Farber 4th ed.

Frequency Distribution ,[object Object],[object Object],Larson/Farber 4th ed. 4 26 – 30 5 21 – 25 8 16 – 20 6 11 – 15 8 6 – 10 5 1 – 5 Frequency Class

Frequency Distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],4 26 – 30 5 21 – 25 8 16 – 20 6 11 – 15 8 6 – 10 5 1 – 5 Frequency Class

Frequency Distribution ,[object Object],[object Object],4 26 – 30 5 21 – 25 8 16 – 20 6 11 – 15 8 6 – 10 5 1 – 5 Frequency Class

Constructing a Frequency Distribution from a Data Set ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example: Constructing a Frequency Distribution ,[object Object],[object Object],Larson/Farber 4th ed.

Solution: Constructing a Frequency Distribution ,[object Object],[object Object],Larson/Farber 4th ed. Round up to 12 50 40 41 17 11 7 22 44 28 21 19 23 37 51 54 42 86 41 78 56 72 56 17 7 69 30 80 56 29 33 46 31 39 20 18 29 34 59 73 77 36 39 30 62 54 67 39 31 53 44

Solution: Constructing a Frequency Distribution Larson/Farber 4th ed. Class width = 12 ,[object Object],[object Object],[object Object],[object Object],19 31 43 55 67 79 Lower limit Upper limit 7

Solution: Constructing a Frequency Distribution ,[object Object],[object Object],[object Object],[object Object],Larson/Farber 4th ed. Class width = 12 30 42 54 66 78 90 18 Lower limit Upper limit 7 19 31 43 55 67 79

Solution: Constructing a Frequency Distribution ,[object Object],[object Object],Larson/Farber 4th ed. Σ f = 50 Class Tally Frequency, f 7 – 18 IIII I 6 19 – 30 IIII IIII 10 31 – 42 IIII IIII III 13 43 – 54 IIII III 8 55 – 66 IIII 5 67 – 78 IIII I 6 79 – 90 II 2

Expanding the Frequency Distribution ,[object Object],[object Object]

Midpoint ,[object Object],[object Object]

Relative Frequency ,[object Object],[object Object],Note: Relative frequency can be written as a decimal or as a percent.

Cumulative Frequency ,[object Object],[object Object]

Example: Midpoints, Relative and Cumulative Frequencies ,[object Object],2 79 – 90 6 67 – 78 5 55 – 66 8 43 – 54 13 31 – 42 10 19 – 30 6 7 – 18 Frequency, f Class

Solution: Midpoints, Relative and Cumulative Frequencies Expanded Frequency Distribution Larson/Farber 4th ed. Σ f = 50 Class Frequency, f Midpoint Relative frequency Cumulative frequency 7 – 18 6 12.5 0.12 6 19 – 30 10 24.5 0.20 16 31 – 42 13 36.5 0.26 29 43 – 54 8 48.5 0.16 37 55 – 66 5 60.5 0.10 42 67 – 78 6 72.5 0.12 48 79 – 90 2 84.5 0.04 50

Example: Midpoints, Relative and Cumulative Frequencies ,[object Object],3 55 – 65 11 44 – 54 7 33 – 43 16 22 – 32 13 11 – 21 5 0 – 10 Frequency, f Class

Solution: Midpoints, Relative and Cumulative Frequencies Expanded Frequency Distribution 55 – 65 44 – 54 33 – 43 22 – 32 11 – 21 0 – 10 Class Σ f = 50 3 11 7 16 13 27 Frequency, f Σ ≈ 1 77 0.0390 60 74 0.1429 49 63 0.0909 38 56 0.2078 27 40 0.1688 16 27 0.3506 5 Cumulative Frequency Relative Frequency Midpoint

2.1 Part 1 - Frequency Distributions

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2.1 Part 1 - Frequency Distributions

Editor's Notes