MA33182 – Basic Mathematics

Chapter 4 – Measures of Dispersion (Range, Interquartile Range, and Quartile Deviation of Ungrouped Data)

Range The range is a measure of variability that shows the difference between the highest and lowest values in a data set. It is a simple way to understand how spread out the data is. To calculate the range, you subtract the smallest value in the set from the largest value. Example: Data set: 3, 7, 8, 15, 22 Range = 22 - 3 = 19 Interquartile Range (IQR) The interquartile range (IQR) measures the spread of the middle 50% of the data. It is the difference between the third quartile (Q3) and the first quartile (Q1). The IQR helps to identify the central tendency and dispersion of the data, minimizing the influence of outliers. Steps to Calculate IQR: 1. Arrange the data in ascending order. 2. Find the first quartile (Q1) - the median of the first half of the data. 3. Find the third quartile (Q3) - the median of the second half of the data. 4. Subtract Q1 from Q3. Example: Data set: 3, 7, 8, 15, 22 Q1 (first quartile) = 7 Q3 (third quartile) = 15 IQR = Q3 - Q1 = 15 - 7 = 8 Quartile Deviation Quartile deviation, also known as the semi-interquartile range, is half of the interquartile range (IQR). It provides a measure of the spread of the data around the median and is less affected by extreme values than the full range. Steps to Calculate Quartile Deviation: 1. Calculate the IQR. 2. Divide the IQR by 2. Example: Data set: 3, 7, 8, 15, 22 IQR = 8 Quartile Deviation = IQR / 2 = 8 / 2 = 4 These concepts help you understand the spread and variability of data, which are essential for statistical analysis and interpreting data sets.