Understanding Mean Deviation:

Mean deviation is a measure of dispersion that calculates the average difference between each data point and the mean of the dataset. It provides an indication of how spread out the data values are from the mean.

Formula for Mean Deviation:

The formula for calculating the mean deviation is as follows:
Mean Deviation = ∑(|x - μ|) / N
Where:
- ∑ denotes the sum of the absolute differences between each data point (x) and the mean (μ)
- N represents the total number of data points in the dataset

Given Information:

In this question, we are given that Q3 (75th percentile) is equal to 40 and Q1 (25th percentile) is equal to 15. These values imply that 25% of the data points fall below 15, while 75% of the data points fall below 40.

Calculating Mean Deviation:

To determine the probable value of mean deviation, we need more information about the dataset. Specifically, we require the values of the individual data points. Without this information, we cannot calculate the mean deviation accurately.

However, we can make some general observations based on the given quartiles. Since Q3 is greater than Q1, we can infer that the dataset is positively skewed, meaning it has a long tail on the right side. This skewness affects the mean deviation.

Impact of Skewness on Mean Deviation:

In a positively skewed dataset, the mean will be greater than the median, and consequently, the mean deviation will also be greater. This is because the mean deviation calculates the average difference from the mean, which is influenced by extreme values on the right side of the distribution.

Therefore, without specific data points, we cannot provide an exact value for the mean deviation. It is essential to have the complete dataset to calculate the mean deviation accurately.

Conclusion:

In conclusion, without the actual data points, we cannot determine the probable value of the mean deviation. However, based on the given quartiles, we can infer that the dataset is positively skewed, which suggests that the mean deviation will be greater than zero. To obtain the precise value of the mean deviation, it is crucial to have the complete dataset.