Measures of Dispersion

8.2

Measures of Dispersion

Range

	Formula

	\(\text{Range} = \text{Largest value} - \text{Smallest value}\)

	Example

	Given a set of data \(36, 25, 15, 26, 50, 27, 20\), determine the range of this set of data

	Solution: 1. Arrange a set of data in ascending order. \(15,20,25,26,27,36,50\) 2. Apply \(\text{Range} = \text{Largest value} - \text{Smallest value}\) \(\therefore 50 -15 = 35.\)

Interquartile range of set of ungrouped data

When the values of a set of data are arranged in ascending order, the first quartile, \(Q_1\) is the value of data that is the first \(\dfrac{1}{4}\) position
While the third quartile, \(Q_3\) is the value of data that is the third \(\dfrac{3}{4}\) position

Variance and standard deviation

Its are the measures of dispersion commonly used in statistics.
The variance is the average of the square of the difference between each data and the mean.
The standard deviation is the square root of variance which is also measures the dispersion of data set relative to its mean.

	Formula

	Variance \(\sigma^2= \dfrac{\sum (x- \bar{x})}{N}\)

	Standard deviation \(\sigma= \sqrt{\dfrac{\sum (x- \bar{x})}{N}}\) or \(\sigma= \sqrt{\dfrac{\sum x^2}{N}-\bar{x}^2}\)

Box Plot

Box plot is a way of showing the distribution of a set of data based on five values, namely the minimum value, first quartile, median, third quartile, and the maximum value of set of data.

	Example of box plot

Measures of Dispersion

8.2

Measures of Dispersion

Range

	Formula

	\(\text{Range} = \text{Largest value} - \text{Smallest value}\)

	Example

	Given a set of data \(36, 25, 15, 26, 50, 27, 20\), determine the range of this set of data

	Solution: 1. Arrange a set of data in ascending order. \(15,20,25,26,27,36,50\) 2. Apply \(\text{Range} = \text{Largest value} - \text{Smallest value}\) \(\therefore 50 -15 = 35.\)

Interquartile range of set of ungrouped data

When the values of a set of data are arranged in ascending order, the first quartile, \(Q_1\) is the value of data that is the first \(\dfrac{1}{4}\) position
While the third quartile, \(Q_3\) is the value of data that is the third \(\dfrac{3}{4}\) position

Variance and standard deviation

Its are the measures of dispersion commonly used in statistics.
The variance is the average of the square of the difference between each data and the mean.
The standard deviation is the square root of variance which is also measures the dispersion of data set relative to its mean.

	Formula

	Variance \(\sigma^2= \dfrac{\sum (x- \bar{x})}{N}\)

	Standard deviation \(\sigma= \sqrt{\dfrac{\sum (x- \bar{x})}{N}}\) or \(\sigma= \sqrt{\dfrac{\sum x^2}{N}-\bar{x}^2}\)

Box Plot

Box plot is a way of showing the distribution of a set of data based on five values, namely the minimum value, first quartile, median, third quartile, and the maximum value of set of data.

	Example of box plot

Measures of Dispersion

Measures of Dispersion

Chapter : Measures of Dispersion of Ungrouped Data

Topic : Measures of Dispersion

Related notes