Mean Deviation of a Normal Curve

A normal distribution is a bell-shaped curve that is symmetrical and characterized by its mean and standard deviation. The mean deviation is a measure of dispersion that calculates the average distance of data points from the mean. In order to calculate the mean deviation of a normal curve, we need to have information about the points of inflection.

Points of Inflection

The points of inflection on a normal curve represent the points where the curve changes concavity. In other words, these points indicate where the curve transitions from being concave upwards to concave downwards, or vice versa. In a normal distribution, there is one point of inflection, which is the mean of the distribution.

Given that the points of inflection of the normal curve are 40 and 60, we can conclude that the mean of the distribution is the midpoint between these two points, which is (40 + 60) / 2 = 50.

Calculating the Mean Deviation

To calculate the mean deviation, we first need to find the deviations of each data point from the mean. In this case, since we only have information about the points of inflection, we can calculate the deviations of these points from the mean.

The deviation of a data point from the mean is the absolute difference between the data point and the mean. Therefore, the deviations of the points of inflection from the mean (50) are:

Deviation of the first point of inflection (40) from the mean: |40 - 50| = 10
Deviation of the second point of inflection (60) from the mean: |60 - 50| = 10

Mean Deviation Formula

The mean deviation is calculated by finding the average of the absolute deviations from the mean. In this case, since we only have two data points, the mean deviation can be calculated as:

Mean Deviation = (Deviation of the first point of inflection + Deviation of the second point of inflection) / Number of data points
Mean Deviation = (10 + 10) / 2
Mean Deviation = 20 / 2
Mean Deviation = 10

Therefore, the mean deviation of the normal curve with the given points of inflection is 10.