To calculate the Standard Deviation (SD):
\[ SD = \sqrt{\frac{1}{N} \sum (x_i - \mu)^2} \]
Where:
Measures of variability, also known as measures of dispersion, are statistical calculations that describe the spread or dispersion of a set of data. They provide information about the range, interquartile range, variance, and standard deviation of the data set. These measures help to understand how much the data points differ from each other and from the central tendency (mean, median, or mode) of the data set. They are essential in statistical analysis to assess the reliability and predictability of data.
Let's assume the following observations:
Using the formula:
Mean (\(\mu\)) = \(\frac{2 + 4 + 4 + 4 + 5 + 5 + 7 + 9}{8} = 5\)
Sum of Squares = \((2-5)^2 + (4-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (5-5)^2 + (7-5)^2 + (9-5)^2 = 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32\)
Variance = \(\frac{32}{8} = 4\)
Standard Deviation (SD) = \(\sqrt{4} = 2\)
The Standard Deviation is 2.
