Range and Quartile Deviation || Lesson 20 || Probability & Statistics || Learning Monkey ||
Range and Quartile Deviation In this class, We discuss Range and Quartile Deviation. The reader should have prior knowledge of the measure of dispersion. Click Here. Range: Example: 8, 5, 16, 33, 7, 24, 5, 30, 33, 37, 30, 9, 11, 26, 32 Arrange the data in ascending order. 5, 5, 7, 8, 9, 11, 16, 23, 24, 26, 30, 30, 32, 3, 37 Range = maximum value – minimum value Range = 37 – 5 = 32 The range is one of the ways to find the measure of dispersion. The range is not used much in the statistics. Quartile Deviation: The reader should have prior knowledge of quartile points. Click Here. Quartile Deviation = (Q3 – Q1)/2 Q3 is upper quartile Q1 is lower quartile. We understand the uses of quartile deviation with an example. Example: 8, 2, 5, 1, 9, 15, 20, 7, 3, 25, 27 Arrange the data in ascending order. 1, 2, 3, 5, 7, 8, 9, 15, 20, 25, 27 n = 11 Q1 = ((n+1)/4) = 3 Q3 = (3(n+1)/4) = 20 QD = (20 – 3) / 2 QD = 8.5 1) Quartile deviation helpful if we need the dispersion of middle 50% data values. 2) Not involving extreme terms. last and first 25% data values. So not affected by outliers. Some times we use quartiles to identify outliers. Interquartile range: IQR = Q3 – Q1 Identifying outliers is helpful in data analysis. The interquartile range is one of the ways to identify outliers. Example: 1, 2, 3, 5, 7, 8, 9, 15, 20, 25, 27 IQR = Q3 – Q1 IQR = 20 – 3 IQR = 17 Outlying points are given as 1) Q1 – 1.5*IQR Below the value, Q1 – 1.5*IQR is considered an outlier. 3 – 1.5*17 = -22.7 We will discuss why we use the value 1.5 in the equation in our later classes when we discuss normal distribution. 2) An outlying point is above the value Q3 + 1.5 * IQR. 20 + 1.5 * 17 = 45.5 Coefficient of Quartile Deviation: The coefficient of quartile deviation is the relative measure of quartile deviation. CQD = (Q3- Q1)/(Q3 + Q1) We use the coefficient of quartile deviation to measure the dispersion of two different distributions. Example: 1) 1, 2, 3, 5, 7, 8, 9, 15, 20, 25, 27 CQD = (Q3- Q1)/(Q3 + Q1) = (20 – 3) (20 + 3) CQD = 0.73 2) 1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11 CQD = (Q3- Q1)/(Q3 + Q1) = (9 – 3) / (9+3) CQD = 0.5 The first data is having more data distribution. Link for playlists: / @wisdomerscse Link for our website: https://learningmonkey.in Follow us on Facebook @ / learningmonkey Follow us on Instagram @ / learningmonkey1 Follow us on Twitter @ / _learningmonkey Mail us @ [email protected]
