Engr/Math/Physics 25
Chp7
Statistics-1
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Histogram and Normal Distribution: Understanding Continuous Data, Slides of Calculus for Engineers
An introduction to histograms and normal distributions, focusing on continuous data. It covers the characteristics of histograms, the concept of bins, numerical output, and histogram commands. Additionally, it discusses normal distributions, their relationship to histograms, and the calculation of probabilities using the error function (erf).
Typology: Slides
2012/2013
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- Engr/Math/Physics
- Chp
- Statistics-
Learning Goals
- Use MATLAB to solve Problems in
- Statistics
- Probability
- Use Monte Carlo (random) Methods to
Simulate Random processes
- Properly Apply Interpolation or
Extrapolation to Estimate values between
or outside of know data points
HistoGram ≡ Frequency Chart
- A HistoGram shows how OFTEN some event
Occurs
- Histograms are
often constructed
using Frequency
Tables
Histograms In MATLAB
- MATLAB has 6 Forms
of the Histogram Cmd
- The Simplest
Hist(y)
The Plot Statement
- Generates a
Histogram with
10 bins
Example: Max Temp
at Oakland AirPort in
Jul-Aug
TmaxOAK = [70, 75, 63, 64, 65, 66, 65, 65, 67, 78, 75, 73, 79, 71, 72, 67, 69, 69, 70, 74, 71, 72, 71, 74, 77, 77, 86, 90, 90, 70, 71, 66, 66, 72, 68, 73, 72, 82, 91, 82, 76, 75, 72, 72, 69, 70, 68, 65, 67, 65, 63, 64, 72, 70, 68, 71, 77, 65, 63, 69, 69, 67]
hist(TmaxOAK), ylabel('No. Days'), xlabel('Max. Temp (°F)'), title('Oakland Airport - Jul-Aug08')
Histograms In MATLAB
- Next Example: Max
Temp at Stockton
AirPort in Jul-Aug
Hist(y)
The Plot Statement
- Generates a
Histogram with
10 bins
TmaxSTK = [94, 98, 93, 94, 91, 96, 93, 87, 89, 94, 100, 99, 103, 103, 103, 97, 91, 83, 84, 90, 89, 95, 94, 99, 97, 94, 102, 103, 107, 98, 86, 89, 95, 91, 84, 93, 98, 104, 105, 107, 103, 91, 90, 96, 93, 86, 92, 93, 95, 95, 86, 81, 93, 97, 96, 97, 101, 92, 89, 92, 93, 94]
hist(TmaxSTK), ylabel('No. Days'), xlabel('Max. Temp (°F)'), title(‘Stockton Airport - Jul-Aug08')
hist Result for Stockton
It was HOT
in Summer
Bin Width =
= 2.6 °F
(^080 85 90 95 100 105 )
2
4
6
8
10
12
14
16 Stockton Airport - Jul-Aug
No. Days
Max. Temp (°F)
hist Plots 17 Bins
hist(TmaxSTK,17),
ylabel('No. Days'), xlabel('Max. Temp (°F)'), title('Stockton, CA - Jul- Aug08')>>
hist(TmaxOAK,17), ylabel('No. Days'), xlabel('Max. Temp (°F)'), title('Oakland, CA - Jul- Aug08')
(^080 85 90 95 100 105 )
1
2
3
4
5
6
7
8
9
10 Stockton, CA - Jul-Aug
No. Days
Max. Temp (°F) 060 65 70 75 80 85 90 95
1
2
3
4
5
6
7
8
9
10 Oakland, CA - Jul-Aug
No. Days
Max. Temp (°F)
hist Plots Same Scale
x = [60:2.5:110]; hist(TmaxSTK,x), ylabel('No. Days'), xlabel('Max. Temp (°F)'), title('Stockton, CA - Jul- Aug08')
x = [60:2.5:110];
hist(TmaxOAK,x), ylabel('No. Days'), xlabel('Max. Temp (°F)'), title('Oakland, CA - Jul- Aug08')
(^060 65 70 75 80 85 90 95 100 105 )
2
4
6
8
10
12
14
16 Oakland, CA - Jul-Aug
No. Days
(^60 65 70 75 80 85 90 95 100 105 110) Max. Temp (°F) 0
2
4
6
8
10
12
14
16 Stockton, CA - Jul-Aug
No. Days
Max. Temp (°F)
hist Numerical Output
- Bin-Count and Bin-Locations (Frequency
Table) for the Oakland Data
[u, v] = hist(TmaxOAK,x) u = 0 3 11 7 15 9 6 4 1 2 1 0 3 0 0 0 0 0 0 0 0 v = 60.0000 62.5000 65.0000 67.5000 70.
72.5000 75.0000 77.5000 80.0000 82. 85.0000 87.5000 90.0000 92.5000 95. 97.5000 100.0000 102.5000 105.0000 107.
Histogram Commands - 1
Command Description
bar(x,y) Creates a bar chart of y versus x.
hist(y)
Aggregates the data in the vector y into
10 bins evenly spaced between the
minimum and maximum values in y.
hist(y,n)
Aggregates the data in the vector y into
n bins evenly spaced between the
minimum and maximum values in y.
hist(y,x)
Aggregates the data in the vector y into
bins whose center locations are
specified by the vector x. The bin widths
are the distances between the centers.
Data Statistics Tool - 1
- Make Line-Plot
of Temp Data
for Stockton,
CA
- Use the Tools
Menu to find
the Data
Statistics Tool
Data Statistics Tool - 2
- Use the Tool
to Add Plot
Lines for
- The Mean
- ±StdDev
Probability
- Probability ≡ The LIKELYHOOD that a
Specified OutCome Will be Realized
- The “Odds” Run from 0% to 100%
- Class Question: What are the
Odds of winning the California MEGA-
MILLIONS Lottery?
175 711 536 ... EXACTLY???!!!
- To Win the MegaMillions Lottery
- Pick five numbers from 1 to 56
- Pick a MEGA number from 1 to 46
- The Odds for the 1 st^ ping-pong Ball
= 5 out of 56
- The Odds for the 2 nd^ ping-pong Ball
= 4 out of 55, and so On
- The Odds for the MEGA are 1 out of 46