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 and the mode of a set of data are 15.7 and 17, respectively. Find the median of the data, using the empirical formula. (Round off to one decimal place)
16.4
15.9
16.1
15
16.1
Use the approximation 3├ЧMedianтЙИMode+2├ЧMean. Since 17+2(15.7)=17+31.4=48.4, dividing 48.4 by 3 gives approximately 16.13.
Mean = 15.7, Mode = 17
Mode=3├ЧMedianтИТ2├ЧMean
Use the approximation 3├ЧMedianтЙИMode+2├ЧMean. Since 17+2(15.7)=17+31.4=48.4, dividing 48.4 by 3 gives approximately 16.13.
Many students mistakenly use the formula 2├ЧMean=3├ЧMedianтИТMode, resulting in incorrect arithmetic due to sign errors.
State the empirical relationship
The relationship between mean, median, and mode for a moderately skewed distribution is given by the empirical formula.
Mode=3├ЧMedianтИТ2├ЧMean
Substitute the known values
Substitute Mean = 15.7 and Mode = 17 into the empirical formula.
17=3├ЧMedianтИТ2├Ч15.7
Solve for the median
Calculate the value of 2├Ч15.7 and then isolate the Median.
17=3├ЧMedianтИТ31.4тЯ╣3├ЧMedian=17+31.4=48.4
Final division
Divide 48.4 by 3 to find the median, rounding to one decimal place.
Median=348.4тАЛтЙИ16.133...тЙИ16.1
C is correct because the application of the empirical formula yields a median of approximately 16.1.
This empirical formula is a standard result in statistics; always remember the coefficient sequence: 1 (Mode), 3 (Median), 2 (Mean).
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