Points of Inflexion of a Normal Curve and Mean Deviation

Introduction:
In statistics, a normal curve or a bell curve is a symmetrical probability distribution that is widely used to model various random variables. The mean deviation, also known as the average deviation, is a measure of dispersion that quantifies the average distance between each data point and the mean of the dataset. In this scenario, we will explore the relationship between the points of inflection of a normal curve and its mean deviation.

Understanding Points of Inflection:
Points of inflection are specific points on a curve where the concavity changes. In the context of a normal curve, these points represent the locations on the curve where the curvature transitions from concave upwards to concave downwards or vice versa. These points divide the curve into different segments with different curvatures.

Mean Deviation and Symmetry:
The mean deviation is calculated by finding the average absolute difference between each data point and the mean of the dataset. In a normal curve, the mean is located at the center of the distribution, and the curve is symmetrical about the mean. This symmetry implies that the mean deviation will be the same on both sides of the mean.

Mean Deviation and Points of Inflection:
Since the points of inflection divide the normal curve into different segments with different curvatures, they also divide the curve into different regions with different mean deviations. The mean deviation will be the same within each segment, but it may differ between segments.

Calculating the Mean Deviation:
To calculate the mean deviation, we need the exact values of the data points in the normal curve. However, in this scenario, only the points of inflection are provided, which are not sufficient to determine the mean deviation.

Conclusion:
In conclusion, the mean deviation of a normal curve cannot be determined solely based on the points of inflection. The mean deviation requires the actual data values of the curve. However, we can infer that the mean deviation will be the same within each segment defined by the points of inflection due to the symmetry of the normal curve. To calculate the mean deviation, it is necessary to have the complete dataset.

Point of inflation are always mean +/-s.d
therefore mean+ s.d =60
mean-s.d=40
solving both eqn mean= 50