What is Skewness? Why is a Curve said to be Skewed? How the Skewness of a Curve measured?

Measures of Skewness

Q.1 Explain the various methods of measuring Skewness.

Skewness measurements are intended to provide information on the direction and degree of asymmetry in a variable. These measurements might be either absolute or relative.

Methods of Measuring Skewness:

    (i)            Karl Pearson’s Measure: This measure is based on statistical averages.

            (a) Absolute Measure (Skewness) (Sk):

Sk = X - Z       or        Sk = 3(X - M)

            (b) Relative Measure or Coefficient of Skewness (J):

                       or

Skewness is represented by an algebraic sign; if it is positive, skewness is positive. Skewness is negative if it is −.

(ii) Bowley’s Measure or Quartiles Measure:

Bowley's skewness metric is known as the second measure of skewness. This measure is helpful in distributions with an ill-defined mode, but it may also be employed in open-ended distributions.

and Coefficient of skewness 

(iii) Kelly’s Measure:

It is derived using percentiles and deciles and is based on 90% of the data.

   Skewness = P90 + P10 – P50              or                         D9 + D1 – D5

and Coefficient of Skewness (Jp) 

= P90 + P10 – P50            or        D9 + D1 – D5

      P90 - P10                                      D9 - D1

Q.2 What is Skewness? Why is a Curve said to be Skewed? How the Skewness of a Curve measured?

Asymmetry or absence of symmetry in the form of a frequency distribution is referred to as skewness. Skewness, in other words, characterises the form of a distribution.

When the mean and median of a distribution fall at opposite locations in the distribution, the centre of gravity is moved to one side or the other — to the left or right.

The concept of skewness will be clear from the following diagrams –

(i)                Normal or Symmetrical Distribution:

The frequency spread is the same on both sides of the curve's centre point. The distribution curve for such a distribution is bell-shaped. Mean, Median, and Mode all have the same value.

(ii)    Asymmetrical or Skewed Distribution: A distribution which is not symmetrical is called a skewed distribution. It can be of two types: 

a)     Positively Skewed Distribution

      In a positively skewed distribution, the curve has a longer tail to the right, the mean is at its highest, the mode is at its lowest, and the median is in the middle.

b)     Negatively Skewed Distribution

In a negatively skewed distribution, the tail is longer to the left, and the value of mode is 'maximum,' while the value of mean is 'minimum,' with the median falling in between the two.    

Negatively & Positively Skewed Distribution

The following tests are used to determine if a distribution is skewed or not.

Skewness is present if – 

- If the mean, median, and mode are not the same.

- If the curve does not have a bell form.

- The quartiles are not equally spaced from the median.

- If the total of the deviations from the median and mode is more than zero, then

- The distribution is skew if the sum of the frequencies on the two sides of the mode is not equal.

Q.3 Give the difference between Dispersion and Skewness.