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# Chapter 16.  Statistics
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# 16.1   Introduction
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# MAPLE SESSION 1
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>    with(stats);
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# 16.2   Data Sets
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#
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# MAPLE SESSION 2
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>    with(stats): 
>    data1 := importdata("data1.dat",2):
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# MAPLE SESSION 3
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>    life := data1[1]: 
>    amount := data1[2]:
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# MAPLE SESSION 4
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>    example_dataset := [10, 20, 30, 30, 30, missing];
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# MAPLE SESSION 5
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>    example_dataset:=[10,20, Weight(30,3), missing];
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# MAPLE SESSION 6
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>    describe[count](life);
>    describe[count](example_dataset);
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# MAPLE SESSION 7
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>    describe[countmissing](life);
>    describe[countmissing](example_dataset);
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# 16.3   Numerical methods for describing data
# 16.3.1   Describing the center of a data set
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#
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# MAPLE SESSION 8
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>    with(stats): 
>    data1:=importdata("data1.dat",2): 
>    life:=data1[1]: 
>    amount:=data1[2]: 
>    describe[mean](life);
>    describe[mean](amount);
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# MAPLE SESSION 9
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>    describe[mean]([10, 20, 30, 30, 30, missing]);
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# MAPLE SESSION 10
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>    describe[median](life);
>    describe[median](amount);
>    describe[median]([10, 20, 30]);
>    describe[median]([10, 20, 30, 40]);
#
#
# MAPLE SESSION 11
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>    describe[mean]([10, 20, 30, 40]), 
>  describe[mean]([10, 20, 30, 1000]);
>    describe[median]([10, 20, 30, 40]), 
>  describe[median]([10, 20, 30, 1000]);
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# MAPLE SESSION 12
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>    with(stats): 
>    describe[mode]([10, 20, 30, 30, 30, missing]);
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# MAPLE SESSION 13
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>    with(stats): 
>    H := describe[harmonicmean]([10, 20, 30, 30, 30, missing]);
>    G := describe[geometricmean]([10, 20, 30, 30, 30, missing]);
>    Q := describe[quadraticmean]([10, 20, 30, 30, 30, missing]);
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# 16.3.2   Describing the dispersion of a data set
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#
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# MAPLE SESSION 14
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>    with(stats): 
>    describe[range]([10, 20, 30, 30, 30, missing]);
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# MAPLE SESSION 15
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>    with(stats): 
>    describe[variance[1]]([10, 20, 30, 30, 30, missing]);
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# MAPLE SESSION 16
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>    with(stats): 
>    describe[variance [0]]([1, 0,-1]), 
>  describe[variance[1]]([1,0,-1]);
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# MAPLE SESSION 17
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>    with(stats): 
>    describe[standarddeviation[1]]([10, 20, 30, 30, 30, missing]);
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# MAPLE SESSION 18
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>    with(stats): 
>    describe[standarddeviation[0]]([1, 0,-1]), 
>  describe[standarddeviation[1]]([1,0, 
>    -1]);
#
#
# MAPLE SESSION 19
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>    with(stats): 
>    data1:=importdata("data1.dat",2): 
>    life:=data1[1]: 
>    describe[range](life); 
>    describe[variance[1]](life); 
>    describe[standarddeviation[1]](life);
#
#
# MAPLE SESSION 20
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>    with(stats): 
>    describe[meandeviation]([10, 20, 30, 30, 30, missing]);
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# MAPLE SESSION 21
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>    with(stats): 
>    describe[percentile[37]]([seq(i,i=1..100)]);
>    describe[percentile[50]]([seq(i,i=1..100)]),
>  describe[median]([seq(i,i=1..100)]);
#
#
# MAPLE SESSION 22
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>    with(stats): 
>    describe[decile[6]]([70,10,80,20,30,40,100,50,60,90]);
>    describe[percentile[2]]([seq(i,i=1..100)]), 
>  describe[percentile[20]]([seq(i,i=1..100)]), 
>  describe[decile[2]]([seq(i,i=1..100)]);
#
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# MAPLE SESSION 23
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>    with(stats): 
>    describe[quantile[1/2]]([1,2,3]);
>    describe[quantile[1/2,1/2]]([1,2,3])=
>  describe[median]([1,2,3]);
>    describe[percentile[20]]([seq(i,i=1..100)])=
>  describe[quantile[20/100]]([seq(i,i=1..100)]);
>    describe[percentile[21]]([seq(i,i=1..100)]),
>  describe[quantile[20/100,.9]]([seq(i,i=1..100)]);
#
#
# MAPLE SESSION 24
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>    with(stats): 
>    describe[quartile[1]]([seq(i,i=1..100)])=
>  describe[percentile[25]]([seq(i,i=1..100)]);
>    describe[quartile[2]]([seq(i,i=1..100)])=
>  describe[percentile[50]]([seq(i,i=1..100)]);
>    describe[median]([seq(i,i=1..100)]);
>    describe[quartile[3]]([seq(i,i=1..100)])=
>  describe[percentile[75]]([seq(i,i=1..100)]);
#
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# MAPLE SESSION 25
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>    with(stats): 
>    IQR1 := describe[quartile[3]]([10, 20, 30, 40])
>  - describe[quartile[1]]([10, 20,30, 40]);
>    IQR2 := describe[quartile[3]]([10, 20, 30, 1000])
>  - describe[quartile[1]]([10, 20, 30, 1000]);
#
# 16.3.3   Describing characteristics of a data set
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#
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# MAPLE SESSION 26
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>    with(stats): 
>    describe[moment[3,0,1]]([10,20,30])=(1/2)*(10^3+20^3+30^3);
>    describe[moment[4,20,1]]([10,20,30])=
>  describe[moment[4,mean,1]]([10,20,30]);
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# MAPLE SESSION 27
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>    with(stats): 
>    describe[moment[3]]([10,20,30])=(1/3)*(10^3+20^3+30^3);
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# MAPLE SESSION 28
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>    with(stats): 
>    describe[sumdata[3]]([10,20,30])=(10^3+20^3+30^3);
>    describe[sumdata]([10,20,30])=(10+20+30);
>    3*describe[moment[4,1,0]]([10,20,30])
>  = describe[sumdata[4,1]]([10,20,30]);
>    `` =  ( (10-1)^4+(20-1)^4+(30-1)^4 );
#
#
# MAPLE SESSION 29
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>    with(stats): 
>    describe[skewness[1]]([-1,0,1]);
>    describe[skewness[1]]([-1,0,1000]): 
>    evalf(%);
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#
# MAPLE SESSION 30
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>    with(stats): 
>    describe[skewness[1]]([-1000,0,1]): 
>    sk1 := evalf(%);
>    describe[skewness[0]]([-1000,0,1]): 
>    sk2 := evalf(%);
>    describe[skewness]([-1000,0,1]): 
>    sk3 := evalf(%);
>    sk1 <> sk2;
>    `` = sk3;
#
#
# MAPLE SESSION 31
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>    with(stats): 
>    data1:=importdata("data1.dat",2): 
>    life:=data1[1]: 
>    amount:=data1[2]: 
>    describe[skewness[1]](life),describe[skewness[1]](amount);
#
#
# MAPLE SESSION 32
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>    describe[kurtosis[1]](life), describe[kurtosis[1]](amount);
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# MAPLE SESSION 33
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>    with(stats): 
>    describe[standarddeviation[1]]([10,20,30])
>  = describe[standarddeviation[1]]([110,120,130]);
#
#
# MAPLE SESSION 34
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>    with(stats): 
>    data1:=importdata("data1.dat",2): 
>    life:=data1[1]: 
>    amount:=data1[2]: 
>    describe[coefficientofvariation[1]]([10,20,30])
>  <> describe[coefficientofvariation[1]]([110,120,130]);
>    describe[coefficientofvariation[1]](life),
>  describe[coefficientofvariation[1]](amount);
#
#
# MAPLE SESSION 35
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>    with(stats): 
>    describe[covariance]([-1,0,1],[-1,0,1]);
>    describe[covariance]([-1,0,1],[1,0,-1]);
#
#
# MAPLE SESSION 36
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>    with(stats): 
>    x1:=[seq(i,i=-10..10)]: 
>    y1:=[seq(i*2,i=-10..10)]: 
>    statplots[scatterplot](x1,y1); 
>    describe[linearcorrelation](x1,y1);
#
#
# MAPLE SESSION 37
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>    x2:=[seq(i,i=-10..10)]: 
>    y2:=[seq(-i,i=-10..10)]: 
>    statplots[scatterplot](x2,y2); 
>    describe[linearcorrelation](x2,y2);
#
#
# MAPLE SESSION 38
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>    x3:=[-1,-1,0,1,1]: 
>    y3:=[1,-1, 0,-1,1]: 
>    statplots[scatterplot](x3,y3): 
>    describe[linearcorrelation](x3,y3);
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#
# MAPLE SESSION 39
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>    describe[linearcorrelation](life, amount);
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# 16.4   Graphical methods for describing data
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#
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# MAPLE SESSION 40
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>    with(stats);