MEASURES OF SKEWNESS

Measure of Skewness– describe the degree of departure of the scores from symmetry.

 Formula:

Skewness can be classified according to the skewness coefficient.

Ø  If the SK < 0, it is called POSITIVELY SKEWED distribution.

Ø  If the SK > 0, it is NEGATIVELY SKEWED distribution.

Ø  If the SK = 0, the scores are NORMALLY distributed.

POSITIVELY SKEWED or the skewed to the right is the distribution where the thin end tail of the graph goes to the right part of the curve.

NEGATIVELY SKEWED or skewed to the left is a distribution where the thin end tail of the graph goes to the left part of the curve.

NORMAL DISTRIBUTION – is a special kind of symmetric distribution and it represents some properties in mathematics. It is very important when comparing between scores and making statistical decisions.

Properties of Normal distribution:

1.   The curve has a single peak, meaning the distribution is unimodal.

2.   It is a bell-shape curve.

3.   It is symmetrical to the mean.

4.   The end tail of the curve can be extended indefinitely in both sides and the asymptotic to the horizontal line.

5.   The shaped of the curve will depend on the value of the mean and standard deviation.

6.   The total area under the curve is 1.0. Hence, the area of the curve in each side of the mean is 0.5.

7.   The probability between two given points in the curve is equal to the area between the two points.

4 types of Standard Scores:

1.   Z-scores – is used to convert a row score to standard score to determine how far a raw score lies from the mean in standard deviation units.

Where:

Analysis:

          The score of Ritz Glenn in Business Calculus is one unit standard deviation below the mean. His score, in Production Management is two units standard deviation above the mean. Therefore, we can conclude that Ritz Glenn performed better in Production Management than Business Calculus

 2.   T-scores – another type of standard score where the mean is 50 and the standard deviation is 10.

Analysis:

          Z-score 0f -1 is equivalent to a T-score of 40, and z-score of +2 is equivalent to a T-score of 70.  The negative value is eliminated in the T-score equivalent. Therefore, Ritz Glenn performed better in Production Management than in the Business Calculus due to higher value of T-score which is equal to 70.

3.  Standard nine (STANINE) – is a nine-point grading scale ranging from 1-9, 1 being the lowest and 9 the highest. Stanine grading is easier to understand than the other standard model.

4.   Percentile Ranks – indicates the percentages of scores that lies below a given scores. If the scores are normally distributed, percentile rank can be inferred from the standard score.

Formula:

Steps in Solving Percentile Ranks:

      1.   Arrange the test scores from highest to lowest.

      2.   Make a frequency distribution of each score and the number of students obtaining each score.

      3.   Find the cumulative frequency by adding the frequency in each score from the bottom upward.

      4.   Find the percentile rank in each score using the formula and the result as indicated in column 

          REFLECTION:

                 Skewness is really useful if we want to measure how many of our students did great in their exam and how many failed. On the other hand, normal distribution helps in comparing between scores and making statistical decisions.