## 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