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Error Bar  

2010-06-10 16:43:04|  分类: 默认分类 |  标签: |举报 |字号 订阅

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  >> help errorbar
ERRORBAR Error bar plot.
    ERRORBAR(X,Y,L,U) plots the graph of vector X vs. vector Y with
    error bars specified by the vectors L and U.  L and U contain the
    lower and upper error ranges for each point in Y.  Each error bar
    is L(i) + U(i) long and is drawn a distance of U(i) above and L(i)
    below the points in (X,Y).  The vectors X,Y,L and U must all be
    the same length.  If X,Y,L and U are matrices then each column
    produces a separate line.
    ERRORBAR(X,Y,E) or ERRORBAR(Y,E) plots Y with error bars [Y-E Y+E].
    ERRORBAR(...,'LineSpec') uses the color and linestyle specified by
    the string 'LineSpec'.  See PLOT for possibilities.
    H = ERRORBAR(...) returns a vector of line handles.
    For example,
       x = 1:10;
       y = sin(x);
       e = std(y)*ones(size(x));
       errorbar(x,y,e)
    draws symmetric error bars of unit standard deviation.

 

The Standard Error of the Average—The Error Bar

There is a mathematical calculation of the uncertainty of the average for a set of data. Since the average is calculated using a set of data that has error, the error of the average also needs to be calculated. The standard error of the average is the measure of how close to the exact value the average is likely to be. It is determined by dividing the standard deviation by the square root of the number of measurements. In mathematical terms:

 

Standard deviation of the average(平均標標準差) = SD/SQRT(n)

For the sample data set above (4.0, 3.9, 4.1, 4.0, 4.2, 3.9, 3.9, 4.1, 3.8, 4.0) SD = 0.12 and the number of observations (n) = 10.

Therefore 0.12/ SQRT(10)= ±0.038

This value is used as the value of the error bars commonly seen on scientific graphs. To draw the error bar for this data point, you would draw a vertical line through the point on the graph with a 0.038 magnitude length above the point and a 0.038 magnitude length below the point, to produce the required .076 magnitude length for the entire bar (the error ranges from -0.038 to +0.038).

 

 

Exercise: Calculate the standard deviation of the average for the class data points for Star X and enter the result in column [H] of Table 10.4. You will use this information in the following chapter

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