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 47 and its median is 61. The mode (using empirical relation) of the data is:
148
111
23
89
89
Calculate the difference between Median and Mean (61тИТ47=14), then add 3├Ч14=42 to the Median (61+28=89) or simply memorize the 3(MedianтИТMean) shift.
Mean = 47, Median = 61
Mode=3├ЧMedianтИТ2├ЧMean
Calculate the difference between Median and Mean (61тИТ47=14), then add 3├Ч14=42 to the Median (61+28=89) or simply memorize the 3(MedianтИТMean) shift.
Students often misremember the empirical relation as Mode=2├ЧMedianтИТ3├ЧMean, which leads to an incorrect negative result.
Identify Empirical Relation
The relationship between Mean, Median, and Mode for a moderately skewed distribution is defined by the Pearson's empirical formula.
Mode=3(Median)тИТ2(Mean)
Substitute the Values
Substitute the given values: Mean = 47 and Median = 61 into the formula.
Mode=3(61)тИТ2(47)
Calculate the Result
Perform the arithmetic operations: 3├Ч61=183 and 2├Ч47=94. Subtracting these gives the final mode.
183тИТ94=89
D is correct because the application of the empirical formula Mode=3(Median)тИТ2(Mean) yields 183тИТ94=89.
This relation is frequently tested in Statistics; remember that for a perfectly symmetrical distribution, Mean=Median=Mode.
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