Repeated Results

If investigations yield identical results in identical conditions, then the results may be accepted as valid. To put it in other words, the validity of results involves obtaining repeated readings of an experimental procedure. The number of readings taken also affects the accuracy of the results, as you will see a little later. Remember that the requirement for repeated results demands that your measuring technique is repeatable too, i.e., your technique would produce identical results when identical quantities are measured.

Mean Value

If you consider the arithmetic mean, x¯, of results for n measurements, of x, i.e., X₁, x₂ ........... x_n, then:

x¯ = x₁ +x₂+ x₃+ ... x_n/n

You can soon see that the greater number of readings (for large value of n), the more accurate will be the result for x. So it is important that repeated results are obtained, although the number of repetitions must be appropriate. It would be appropriate in the case of the pipette calibration experiment to repeat the readings, say, ten times when the final result has only to be within k0.03 cm³ of 25.00 cm³.

Standard Deviation

Standard deviation (SD) is the average amount by which results deviate from the mean value. SD simply gives an indication of how much the data is spread. Arithmetically, SD a,,i-s, fo und as follows:

Where x¯ = mean value

and n = total number of results of x.

Most scientific calculators now-a-days have an SD function built in. s, is the symbol used for the SD of large number of results; i.e., hundreds or more. s_n-1 is used for a few results - and this is the one you should use.