Empirical relation(mean, median and mode)

Empirical relation(mean, median and mode)

1. EMPIRICAL RELATION ( Mean , Median and Mode ) NADEEM UDDIN ASSOCIATE PROFESSOR OF STATISTICS https://www.slideshare.net/NadeemUddin17 https://nadeemstats.wordpress.com/listofbooks/

2. i) Median lies between mean and mode. ii) Median closer to mean than mode. iii) In the case of a moderately skewed distribution, the difference between mean and mode is equal to three times the difference between the mean and median . In moderately skewed distribution, the following approximate relation holds good.   Mean – Mode = 3 (Mean – Median ) OR Mode = 3 Median – 2 Mean This empirical relation does not hold in case of a J – shaped or an extremely skewed distribution.

3. Example -1   For a certain frequency distribution, the mean was 40.5 and median 36. Find the mode using the formula connecting the three. Solution : Given that : Mean = 40.5, Median = 36, Mode = ? We know that : Mean – Mode = 3 (Mean – Median ) 40.5 – Mode = 3 (40.5 – 36 ) 40.5 – Mode = 3  4.5 40.5 – Mode = 13.5 Mode = 40.5 – 13.5 Mode = 27

4. Example -2   For a certain frequency distribution, the mode was 27 and median 36. Find the mean using the formula connecting the three. Solution : Given that: Median = 36, Mode = 27 , Mean = ? We know that : Mode = 3Median - 2Mean 27 = 3 (36) - 2Mean 27 = 108 - 2Mean 27 - 108 = - 2Mean - 81 = - 2Mean  

5. Example -3   For a certain frequency distribution, the mode was 27 and mean 40.5. Find the median using the formula connecting the three. Solution : Given that: Mode = 27 , Mean = 40.5, Median = ? We know that: Mode = 3Median - 2Mean 27 = 3Median – 2(40.5 ) 27 = 3Median – 81 27 + 81 = 3Median 108 = 3Median  

6. DO YOURSELF  i) In a moderately asymmetrical series, the value of arithmetic mean and median is 20 and 18.67 respectively. Find out the value of Mode . (Answer = 16.01) ii) In a moderately skewed distribution, mode = 10 and median = 30, then find the mean. (Answer = 40) iii) In a moderately asymmetrical distribution the mode and mean are 32.1 and 35.4 respectively. Calculate the median . (Answer = 34.3)