Notes on Statistics and Data Analysis - Lecture File 2 | MATH 243, Study notes of Probability and Statistics

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From histograms to density curves Data: 12 17 21 23 24 26 29 31 31 39Histogram with class width 10:

N. Christopher Phillips ()^123456 10 Math 243: Lecture File 2^20 30 40 2 April 2009 2 / 48

From histograms to density curves Data: 12 17 21 23 24 26 29 31 31 39Histogram with class width 10:

Area of red bar: 10 N. Christopher Phillips ()^123456 · 2 = 20.^10 Math 243: Lecture File 2^20 30 40 2 April 2009 2 / 48

From histograms to density curves Data: 12 17 21 23 24 26 29 31 31 39Histogram with class width 10:

Area of red bar: 10 Total area: N. Christopher Phillips ()^123456 · 2 = 20.^10 Math 243: Lecture File 2^20 30 40 2 April 2009 2 / 48

From histograms to density curves Data: 12 17 21 23 24 26 29 31 31 39Histogram with class width 10:

Area of red bar: 10 Total area: 10 Fraction of the data covered by the red bar: 20 N. Christopher Phillips · 2 + 10 ()^123456 · 2 = 20 · 5 + 10.^10 Math 243: Lecture File 2 · 3 = 100^20. /^30 100 = 0^. 240. 2 April 2009 2 / 48

Rescale vertical axis so that total area is 1 (continued)

Area of red bar: 10^ 0.01^ 0.02^ 0.03^ 0.04^ 0.05^ 0.06 · 0 .02 = 0^10.^2.^20 30

N. Christopher Phillips () Math 243: Lecture File 2 2 April 2009 4 / 48

Rescale vertical axis so that total area is 1 (continued)

Area of red bar: 10 Total area:^ 0.01^ 0.02^ 0.03^ 0.04^ 0.05^ 0.06 · 0 .02 = 0^10.^2.^20 30

N. Christopher Phillips () Math 243: Lecture File 2 2 April 2009 4 / 48

Rescale vertical axis so that total area is 1 (continued)

Area of red bar: 10 Total area: 10 The fraction of the data covered by the red bar is still 0just the area of the red bar. · 0.01^ 0.02^ 0.03^ 0.04^ 0.05^ 0.06 0 .02 + 10 · 0 .02 = 0 · 010 .05 + 10.^2. ·^20 0 .03 = 1.^30. 240 , but this is now

N. Christopher Phillips () Math 243: Lecture File 2 2 April 2009 4 / 48

• Math 243: Lecture File 2 N. Christopher Phillips2 April
• N. Christopher Phillips () Math 243: Lecture File 2 2 April 2009 1 /
• Rescale vertical axis so that total area is - 12345610 20 30
  • N. Christopher Phillips 0.01 0.02 0.03 0.04 0.05 0.06 () 10 Math 243: Lecture File 2^20 30 40 2 April 2009 3 /
• Data: - 12345610 20 30
  • N. Christopher Phillips 0.5 1.0 1.5 2.0 2.5 3.0() 10 Math 243: Lecture File 2^20 30 40 2 April 2009 5 /

Data: 12 17 21 23 24 26 29 31 31 39Histogram with class width 5:

Area of red section: N. Christopher Phillips 0.5^ 1.0^ 1.5^ 2.0^ 2.5^ 3.0() 10 Math 243: Lecture File 2^20 30 40 2 April 2009 6 / 48

Data: 12 17 21 23 24 26 29 31 31 39Histogram with class width 5:

Area of red section: 5 N. Christopher Phillips 0.5^ 1.0^ 1.5^ 2.0^ 2.5^ 3.0() · 1 + 5^10 ·^ Math 243: Lecture File 21 = 10.^20 30 40 2 April 2009 6 / 48

Data: 12 17 21 23 24 26 29 31 31 39Histogram with class width 5:

Area of red section: 5 Total area: 5 N. Christopher Phillips · 1 + 5 0.5^ 1.0^ 1.5^ 2.0^ 2.5^ 3.0() · 1 + 5 · 1 + 5 ·^10 3 +·^ Math 243: Lecture File 21 = 10 · · · = 50.^20. 30 40 2 April 2009 6 / 48

Data: 12 17 21 23 24 26 29 31 31 39Histogram with class width 5:

Area of red section: 5 Total area: 5 Fraction of the data covered by the red section: 10 N. Christopher Phillips · 1 + 5 0.5^ 1.0^ 1.5^ 2.0^ 2.5^ 3.0() · 1 + 5 · 1 + 5 ·^10 3 +·^ Math 243: Lecture File 21 = 10 · · · = 50.^20. 30 /50 = 0^40. 2 .2 April 2009 6 / 48