Discussion
Which of the following will have mean = median = mode ?
Answer: C
The answer is the Normal distribution.
The normal distribution is perfectly symmetrical and bell-shaped, with a single peak at its centre. The peak is the mode, the centre divides the area in half (the median), and the balance point is the mean, so all three coincide.
The Poisson and exponential distributions are positively skewed, with the mean pulled to the right of the mode. A binomial distribution is symmetrical only in the special case p = 0.5 and skewed otherwise, so it does not always have mean = median = mode.
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