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
If the median and the mode are given as 65 and 60, respectively, find the mean.
62.5
68
70
67.5
67.5
Use the mnemonic 'Mo = 3Me - 2Xbar'. Since Mode is 5 less than Median, Mean must be positioned such that it balances the relationship; calculate mentally: 2├ЧMean=3(65)тИТ60=195тИТ60=135.
Median (MdтАЛ) = 65, Mode (MoтАЛ) = 60.
Mode=3├ЧMedianтИТ2├ЧMean
Use the mnemonic 'Mo = 3Me - 2Xbar'. Since Mode is 5 less than Median, Mean must be positioned such that it balances the relationship; calculate mentally: 2├ЧMean=3(65)тИТ60=195тИТ60=135.
Many students accidentally use the formula Mean=3├ЧMedianтИТ2├ЧMode or misarrange the terms, leading to incorrect subtraction.
State the empirical relationship
The relationship between Mean, Median, and Mode for a moderately skewed distribution is defined by the Pearson's empirical formula.
Mode=3├ЧMedianтИТ2├ЧMean
Substitute the given values
Substitute the provided values Mode=60 and Median=65 into the formula.
60=3(65)тИТ2├ЧMean
Solve for Mean
Calculate the product 3├Ч65=195 and rearrange to isolate the Mean: 2├ЧMean=195тИТ60=135.
Mean=2135тАЛ=67.5
D is correct because applying the empirical formula yields a Mean value of 67.5.
This empirical relation is frequently tested in exams; remember that for a perfectly symmetrical distribution, Mean=Median=Mode. If the data is skewed, this formula is the primary tool to relate them.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants