**Mean Deviation**

Mean deviation is a measure of dispersion or spread of a dataset. It measures the average distance between each data point and the mean of the dataset.

**Formula for Mean Deviation**

The formula for mean deviation is as follows:

Mean Deviation = (1/n) * Σ|X - μ|

Where:
- n is the number of data points
- X represents each data point in the dataset
- μ is the mean of the dataset

**Quartile Deviation**

Quartile deviation is another measure of dispersion that represents the spread of data around the median. It is the difference between the upper quartile (Q3) and the lower quartile (Q1) of a dataset.

**Formula for Quartile Deviation**

The formula for quartile deviation is as follows:

Quartile Deviation = (Q3 - Q1) / 2

Where:
- Q3 is the upper quartile
- Q1 is the lower quartile

**Relationship between Mean Deviation and Quartile Deviation**

To find the quartile deviation, we need to know the values of Q3 and Q1. Unfortunately, the mean deviation alone does not provide enough information to directly calculate the quartile deviation.

However, we can make an assumption based on the properties of a normal distribution. In a normal distribution:
- The mean, median, and mode are all equal.
- The median is the same as the second quartile (Q2).

Therefore, we can estimate Q2 as the mean (μ). Since the quartile deviation is the difference between Q3 and Q1, and Q3 and Q1 are equidistant from Q2, we can assume that Q3 and Q1 are equidistant from the mean (μ).

So, we can estimate Q3 and Q1 as follows:
- Q3 = μ + (mean deviation)
- Q1 = μ - (mean deviation)

Now that we have the values of Q3 and Q1, we can calculate the quartile deviation using the formula mentioned earlier.

**Example**

Let's say the mean deviation of a normal variable is 16. To find the quartile deviation, we can estimate Q3 and Q1 as follows:

Q3 = μ + (mean deviation) = μ + 16
Q1 = μ - (mean deviation) = μ - 16

Once we have the values of Q3 and Q1, we can calculate the quartile deviation using the formula:

Quartile Deviation = (Q3 - Q1) / 2

Please note that this estimation assumes that the data follows a normal distribution and that the mean deviation is symmetrically distributed around the mean. In reality, the quartile deviation may vary depending on the actual distribution of the data.