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If the mean and the median pertaining to a certain character of a population are of the same value, which of the following is most likely to occur
A
a bi-modal distribution
B
a T-shaped curve
C
a skewed curve
D
a normal distribution
Detailed Solution
The mean is the arithmetic average of all the values, and the median is the middle value when the values are arranged in order.
In a normal distribution the values are distributed symmetrically on both sides of the central value, giving a bell-shaped curve.
Because of this symmetry, the mean, the median and the mode coincide in a normal distribution.
In a skewed curve the distribution is not symmetrical, and the mean is pulled towards the longer tail, so the mean and the median differ.
A bi-modal distribution has two peaks, and a T-shaped curve is not a frequency distribution of this kind.
Many characters of a population, such as height, show this kind of continuous variation.
So when the mean and the median have the same value, a normal distribution is most likely.
In a normal distribution the values are distributed symmetrically on both sides of the central value, giving a bell-shaped curve.
Because of this symmetry, the mean, the median and the mode coincide in a normal distribution.
In a skewed curve the distribution is not symmetrical, and the mean is pulled towards the longer tail, so the mean and the median differ.
A bi-modal distribution has two peaks, and a T-shaped curve is not a frequency distribution of this kind.
Many characters of a population, such as height, show this kind of continuous variation.
So when the mean and the median have the same value, a normal distribution is most likely.