Mean Deviation:

Mean deviation is a measure of the dispersion or spread of a set of data values around their mean. It gives us an idea of how much the individual data points deviate or differ from the mean. In other words, it quantifies the average distance of each data point from the mean.

Mean Deviation of a Normal Variable:

In the context of a normal variable, the mean deviation represents the average absolute deviation of the data points from the mean. Since the normal distribution is symmetric, the mean deviation is the same as the average absolute deviation from the mean.

Properties of the Normal Distribution:

Before we delve into the calculation of the mean deviation of a normal variable, let's briefly discuss some key properties of the normal distribution:

1. Bell-shaped curve: The normal distribution is characterized by a symmetrical bell-shaped curve, with the mean at the center.

2. Mean and median coincide: The mean and median of a normal distribution are equal, located at the center of the distribution.

3. Standard deviation: The standard deviation measures the spread or dispersion of the data points around the mean. It is a measure of the average distance of each data point from the mean.

Calculation of Mean Deviation:

The mean deviation can be calculated using the following steps:

Step 1: Find the mean of the data set.

Step 2: Subtract the mean from each data point to obtain the deviations.

Step 3: Take the absolute value of each deviation to get the absolute deviations.

Step 4: Calculate the mean of the absolute deviations.

Mean Deviation of a Normal Variable:

In the case of a normal variable, where the mean deviation is given as 16, it means that on average, each data point deviates from the mean by 16 units. This implies that the spread of the data points around the mean is relatively large, with a considerable average distance between each data point and the mean.

Visually Appealing Summary:

To summarize, the mean deviation of a normal variable is a measure of the average absolute deviation of the data points from the mean. In the case where the mean deviation is 16, it indicates a relatively large spread of the data points around the mean. The normal distribution, characterized by its bell-shaped curve, provides insights into the distribution of data points and helps in understanding the level of variability within the dataset.