Civil Engineering > GATE 2018 SET-2 > Probability
A probability distribution with right skew is shown in the figure.
The correct statement for the probability distribution is
A
Mean is equal to mode
B
Mean is greater than median but less than mode
C
Mean is greater than median and mode
D
Mode is greater than median

Correct : c

The correct answer is Option C - Mean is greater than median and mode.
For any skewed distribution, the relationship between mean, median, and mode follows a predictable pattern based on the direction of the skew. This is one of those facts that''s worth memorizing directly for GATE.
In a right-skewed (positively skewed) distribution, the tail stretches toward the right - meaning there are a few very large values pulling the distribution to the right. The mode sits at the peak (the most frequent value), the median lies slightly to the right of the mode, and the mean gets pulled the furthest right by those extreme high values in the tail.
The order is: Mode < Median < Mean
This directly confirms Option C - the mean is greater than both the median and the mode.
Option A (mean equals mode) is only true for a perfectly symmetric distribution - not a skewed one.
Option B (mean greater than median but less than mode) describes the wrong order - this would imply Mode > Mean, which is the left-skew pattern, not right-skew.
Option D (mode greater than median) is also incorrect for a right-skewed distribution - the mode is actually the smallest of the three here.

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Related Topics

right skewed distribution GATE 2018 GATE civil 2018 Set-2 Q13 mean median mode relationship positive skew statistics right skew probability mean greater than median mode skewness GATE civil probability distribution statistics GATE civil engineering 2018

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