Population Sample Standard Deviation Measure of the average amount by which observations deviate on either side of the mean. Standard deviation: measures the variation of a variable in the sample.Return to original units rather than squared units.To “undo” the squaring of difference scores, take the square root of the variance.Lends itself to computation of other stable measures (and is a prerequisite for many of them). Use the computational formula to calculate the variance.Population Sample Variance: Computational Formula In order to make this number not 0, square the difference scores ( negatives to become positives).The average amount that a score deviates from the typical score.STANDARD DEVIATION: “ ROOT- MEANS-SQUARE-DEVIATIONS” VARIANCE: Deviations of each observation from the mean, then averaging the sum of squares of these deviations. Locating Percentiles in a Frequency Distribution 25% included here 25th percentile 50% included here 50th percentile 80thpercentile 80% included here Another type of percentile :The lower quartile is 25th percentile and the upper quartile is the 75th percentile.The median is the 50th percentile: 50% of the cases fall below it.The 75th percentile is a score below which 75% of the cases fall.A percentile is a score below which a specific percentage of the distribution falls.Locating Percentiles in a Frequency Distribution But the most common are 25th (1st Quartile) and 75th (3rd Quartile) Median is 50th percentile: 50% of values lie at or below the median.
Maximum is 100th percentile: 100% of values lie at or below the maximum.Quartiles: Inter quartile : IQR = Q3 – Q1 The following figure shows the interaction between the quartiles, the median and the inter quartile range.50% of the observations in the distribution are in the inter quartile range.Influenced by sample size (the larger the sample, the larger the range). Measure of the average amount by which observations deviate from the mean.Mean of all squared deviations from the mean.Difference between the smallest and largest observations.A single summary figure that describes the spread of observations within a distribution.Measures of Dispersion or Measures of Variability
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