After measuring some experimental quantity 10 times, you work out the statistics (e.g., average, standard deviation, standard error) for this measurement. You then measure the same quantity an additional 30 times, for 40 trials total. Again, you work out the statistics now using all 40 trials. Which of these will change appreciably when working out the statistics using the larger number of trials?
A. Average
B. Standard Deviation
C. Standard Error of the Average
D. Systematic Error

Several statistics can be calculated from values of an experiment. The standard error of average would change appreciably when working out the statistics using the larger number of trials

Of the given options, the standard error of average would have the highest change.

The proof is as follows;

As the sample size changes, the mean and the standard deviation would change (but the change in the mean and standard deviations are negligible)
As sample size changes, the changes in the standard error would be noticed, and its value becomes smaller.

The standard error is calculated using:

[tex]SE = \frac{\sigma}{\sqrt n}[/tex]

Assume:

[tex]\sigma = 10[/tex] when n = 10

The standard error would be:

[tex]SE_1 = \frac{10}{\sqrt{10}} = 3.162[/tex]

When n becomes 40, assume [tex]\sigma = 9.8[/tex]

The standard error would be:

[tex]SE_2 = \frac{9.8}{\sqrt{40}} = 1.550[/tex]

By compare the values of the standard error in both cases, we can conclude that option (c) is correct.

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