Contents

Aaron Klapheck

% Quizz 1       due: 4-Feb-08
clear, clc
Date = date

Date =

30-Jan-2008

Data

x = [30.00, 28.00, 20.00, 22.80, 20.80, 18.60, 20.00, 24.00, 24.00, ...
    16.00, 16.00, 11.60, 22.00, 16.00, 25.00, 20.00, 16.00, 19.00, ...
    19.50, 25.80, 23.60, 24.80, 16.00, 15.80, 17.00, 19.50, 18.10, ...
    19.20, 22.00, 12.00, 20.10, 13.20, 20.00, 28.40, 18.40, 20.00, ...
    16.40, 13.00, 27.00, 10.00, 18.80, 15.60, 10.00, 16.00, 14.60, ...
    18.00, 12.00, 14.40, 11.20, 18.20, 22.00, 25.20, 15.20, 12.40, ...
    18.00, 14.00, 18.00, 16.40, 20.00, 10.00, 18.00, 18.00, 20.50, ...
    12.20, 20.00, 21.60, 16.00, 16.80, 16.40, 20.90, 16.50, 20.80, ...
    18.00, 16.80, 26.50, 24.00, 16.90, 22.40, 15.30, 20.20, 18.00, ...
    20.00, 18.40, 19.00, 18.00, 20.00, 23.90, 21.20, 32.00, 13.50, ...
    10.40, 12.00, 20.00, 23.40, 31.00, 32.00, 15.80, 24.00, 25.60, ...
    28.00, 16.00, 28.00, 27.50, 16.00, 16.00, 16.00, 19.60, 16.00, ...
    22.00, 16.00, 24.00, 12.00];

% sorts the data in vecter x from lowest value to highest value.
Sorted = sort(x)

Sorted =

  Columns 1 through 9 

   10.0000   10.0000   10.0000   10.4000   11.2000   11.6000   12.0000   12.0000   12.0000

  Columns 10 through 18 

   12.0000   12.2000   12.4000   13.0000   13.2000   13.5000   14.0000   14.4000   14.6000

  Columns 19 through 27 

   15.2000   15.3000   15.6000   15.8000   15.8000   16.0000   16.0000   16.0000   16.0000

  Columns 28 through 36 

   16.0000   16.0000   16.0000   16.0000   16.0000   16.0000   16.0000   16.0000   16.0000

  Columns 37 through 45 

   16.4000   16.4000   16.4000   16.5000   16.8000   16.8000   16.9000   17.0000   18.0000

  Columns 46 through 54 

   18.0000   18.0000   18.0000   18.0000   18.0000   18.0000   18.0000   18.1000   18.2000

  Columns 55 through 63 

   18.4000   18.4000   18.6000   18.8000   19.0000   19.0000   19.2000   19.5000   19.5000

  Columns 64 through 72 

   19.6000   20.0000   20.0000   20.0000   20.0000   20.0000   20.0000   20.0000   20.0000

  Columns 73 through 81 

   20.0000   20.0000   20.1000   20.2000   20.5000   20.8000   20.8000   20.9000   21.2000

  Columns 82 through 90 

   21.6000   22.0000   22.0000   22.0000   22.0000   22.4000   22.8000   23.4000   23.6000

  Columns 91 through 99 

   23.9000   24.0000   24.0000   24.0000   24.0000   24.0000   24.8000   25.0000   25.2000

  Columns 100 through 108 

   25.6000   25.8000   26.5000   27.0000   27.5000   28.0000   28.0000   28.0000   28.4000

  Columns 109 through 112 

   30.0000   31.0000   32.0000   32.0000

Part a.

% Creat 12 bins each with length 2.
lenghts = [10:2:32];

% Plot the Histogram.
hist( Sorted, lenghts), xlabel('Values of data'), ...
    ylabel('Absolute Frequency'), title('Absolute Frequency Histogram')

Part b.

% Calculate the mean

% mean = summation(x)/n.
% where x = each data value and n = total number of data points.

Mean = mean(Sorted)

Mean =

   19.1312

Part c.

% Calculate the variance

% variance = summation((x - x_bar)^2)/(n-1).
% where x = each data value, x_bar = average value,
% and n = total number of data points.

% variance = (standard deviation)^2

variance = (std(Sorted))^2

variance =

   24.5744

Part d.

% Calculate the standard deviation

% standard deviation = (variance)^(1/2)

Standard_deviation = (variance)^(1/2)

Standard_deviation =

    4.9573

Part e.

% Determine the median

% median = value in the middle

% there is no middle value because the total number of values is an even
% number. Because of this we will take the average of the 56th and 57th
% value to obtain the median.

%        (56th value + 57th value)/2
Median = (Sorted(56) + Sorted(57))/2

% check
Median_check = median(Sorted)

Median =

   18.5000


Median_check =

   18.5000

Part f.

% Determine the mode

% mode = the value that appears the most

% 16.00 appears the most number of times (11 times).

disp('Mode = 16.00')

Mode = 16.00

Part g.

% Determine the 25th percentile

% Gole: to find the value that is larger than 25% of the given values
% (this value will also be smaller than 75% of given values).

% Solution: multiply the (percentage larger than) value by the (total
% length) value to find the postition of the desired value. Once the
% position is known, simply display the value located at this position.

position = 0.25*length(Sorted)

TwontyFifthPercentile = Sorted(position)

position =

    28


TwontyFifthPercentile =

    16

Part h.

% Determine the 75th percentile

% Gole: to find the value that is larger than 75% of the given values
% (this value will also be smaller than 25% of given values).

% Solution: multiply the (percentage larger than) value by the (total
% length) value to find the postition of the desired value. Once the
% position is known, simply display the value located at this position.


position = 0.75*length(Sorted)

SeventyFifthPercentile = Sorted(position)

position =

    84


SeventyFifthPercentile =

    22

Published with MATLAB® 7.0.1