Standard Deviation in Language Assessment

Standard Deviation in Language AssessmentTSL 3123DefinitionThe standard deviation is a measure of statistical dispersion.

Statistical dispersion variability /spread; denotes how stretched or squeezed the distribution can be.

.. how far from the normal.Getting thereMeanVarianceStandard deviation

Finding the meanThe heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.

Mean = 600 + 470 + 170 + 430 + 300 = 1970 = 39455so the mean (average) height is 394 mm. Let's plot this on the chart:

Finding the varianceTo calculate the Variance, take each difference, square it, and then average the result:

206, 76, -224, 36, -94

So, the Variance is21,704.and the Standard Deviation is just the square root of Variance

Finding the standard deviationStandard Deviation: = 21,704 = 147.32...=147(to the nearest mm)

The mean represents a statistical average of individual performanceThe score of an individual may not exactly correspond to the mean; it may deviate, or be different from, the mean. The extent to which an individuals score deviates away from the mean is called the standard deviation.A teacher would want to know this information because it might change how he or she teaches the material or how he or she constructs the test. SummaryA standard deviation is a number that indicates how much a group of scores vary from one another on average. Another way to say this is that the standard deviation tells you the standard, or typical, amount that scores in a group deviate, or change, within that group.