Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
The mean of a data is 35 and its median is 40. The mode (using empirical relation) of the data is:
45
50
55
60
50
Remember the mnemonic '3 Median - 2 Mean = Mode'. Just multiply the median by 3 (120) and subtract twice the mean (70) to get 50.
Mean = 35, Median = 40
Mode=3├ЧMedianтИТ2├ЧMean
Remember the mnemonic '3 Median - 2 Mean = Mode'. Just multiply the median by 3 (120) and subtract twice the mean (70) to get 50.
Students often swap the coefficients and calculate 2├ЧMedianтИТ3├ЧMean leading to an incorrect result.
State the Empirical Relation
The relationship between the three measures of central tendency for a moderately skewed distribution is given by the Pearson's empirical formula.
Mode=3├ЧMedianтИТ2├ЧMean
Substitute the Given Values
Substitute the given values of Mean = 35 and Median = 40 into the formula.
Mode=3(40)тИТ2(35)
Perform Calculation
Calculate the products first and then find the difference.
Mode=120тИТ70=50
B is correct because applying the empirical formula 3├Ч40тИТ2├Ч35 yields 50.
This relation is highly useful in exams to quickly estimate the mode when the frequency distribution is not fully provided; it frequently appears in Data Interpretation sections.