SaiBook.us Statistics

Lesson Example Discussion Quiz: Class Homework

Lesson

Title: Karl pearson’s coefficient of skewness

Grade: 9-a Lesson: S2-L7

Explanation: Hello students, let us learn a new topic in statistics today with definitions, concepts, examples, and worksheets included.

Lesson:

Definition: Skewness:

Skewness means lack of symmetry. We study skewness to have an idea about the shape of the curve drawn from the given data.
When the data set is not a symmetrical distribution, it is called a skewed distribution and such a distribution could either be positively skewed or negatively skewed.

$1$

Explanation:

The concept of skewness will be clear from the following three diagrams:

Symmetrical distribution: It is clear from the diagram below that in a symmetrical distribution the values of mean, median and mode coincide. The spread of the frequencies is the same on both sides of the centre point of the curve

Positively skewed distribution : If the mean exceeds the mode and median (Mode < Median < Mean) then the distribution is positively skewed. In other words, if the coefficient of skewness is positive then the distribution is skewed to the right.

Negatively skewed distribution: If the mode exceeds the median and mean (Mean < Median < Mode) then the distribution is negatively skewed. Thus, the coefficient of skewness will be negative and the distribution will be skewed to the left.

Definition: Karl-Person coefficient of skewness:

This method is most frequently used for measuring skewness.
The value of this coefficient would be zero in a symmetrical distribution.
If mean is greater than mode, coefficient of skewness would be positive otherwise negative.

$2$

Explanation:

Pearson’s first and second coefficients of skewness are two common methods.
Pearson’s first coefficient of skewness, or Pearson mode skewness, subtracts the mode from the mean and divides the difference by the standard deviation.This is most frequently used for calculating skewness.
Pearson’s second coefficient of skewness, or Pearson median skewness, subtracts the median from the mean, multiplies the difference by three, and divides the product by the standard deviation.