Concerning distribution of scores what is the significance o

Concerning distribution of scores, what is the significance of determining basic measures of variability involving a percentile, a stanine, and a standardized score (i.e., t-score, z- score)?

Solution

Percentile in a distribution helps us a comparative analysis.

For example, if 6000 seats are available for a educaitonal programme and 10000 people compete, instead of fixing pass marks percentile is fixed as

admission to those who come in the top 6000. Or percentile is 40 for cut off score below

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Stanine: In this method, for example, test scores are first ranked from lowest to the highest

Then a stanine value of 1,2.... is given as say from 0 to 4% stanine 1, 5 to 10 % stanine 2 etc.

This helps us like weighted method of comparing and filtering.

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A t score normally used for comparison with hypothesised value is used when sample size is less than 30 and also when population std deviation is not known

But a z score is used when population std dev is known and also when sample size is more than 30.