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Class 824 Class 924 Class 1036

SubjectAll Physics 19 Chemistry 19 Biology 19 Mathematics 27

ChapterAll Arithmetic Progressions Circles Coordinate Geometry Introduction to Trigonometry Pair of Linear Equations in Two Variables Polynomials Probability Quadratic Equations Real Numbers Some Applications of Trigonometry Statistics Surface Areas and Volumes Triangles

Showing 1 question in Mathematics for Class 10. Tap a card to reveal the answer.

MathematicsStatisticsmedium

The mean of a distribution is 27 and its median is 30. Estimate the mode using the empirical relationship.

Reveal answer ↓

What it is

For a moderately skewed data set, the three averages link as Mode = 3 Median - 2 Mean.

Answer

The empirical relationship between the three measures of central tendency is Mode = 3 Median - 2 Mean. Substituting, Mode = 3(30) - 2(27) = 90 - 54 = 36.

Mode = 3 Median - 2 Mean

•Mode = 3 Median - 2 Mean
•= 3(30) - 2(27)
•= 90 - 54 = 36

Why learn this

It estimates the most common value from the other two - handy in surveys and economics.

💡 Memory trick

Mode = 3 Median - 2 Mean ('3M minus 2-Mean gives the Mode').