Measures of variability , define and give examples
Measures of variability, also known as measures of dispersion, are statistics that describe the spread or dispersion of a set of data points. They provide information about how much data points vary or deviate from the central tendency.
Some common measures of variability include:
1. Range: The range is the difference between the maximum and minimum elements in a data set. For example, if a data set consists of the numbers {2, 4, 6, 8, 10}, the range would be 10 - 2 = 8.
2. Interquartile Range (IQR): The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1) in a data set. It gives a measure of the spread of the middle 50% of data points. For example, if the data set {1, 3, 5, 7, 9} was divided into quartiles, Q1 would be 3, Q3 would be 7, and the IQR would be 7 - 3 = 4.
3. Variance: Variance is the average of the squared differences between each data point and the mean of the data set. It provides a measure of how spread out the data points are around the mean.
4. Standard Deviation: The standard deviation is the square root of the variance. It is a commonly used measure of dispersion that provides information about how spread out the data points are from the mean.
These measures of variability are important in statistical analysis as they help to provide a more comprehensive understanding of the distribution of data points in a data set.