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 =

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/ = ±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.