What is average deviation ? Compute average deviation for the following data : 12, 31, 42, 36, 41, 32, 41, 71, 10, 11.

1. Introduction

Average deviation is a measure of variability that quantifies the average distance of data points from the mean of the dataset. It provides insights into the dispersion of data around the central tendency. Calculating average deviation involves finding the absolute differences between each data point and the mean, then averaging these differences.

2. Calculation of Average Deviation

Step 1: Calculate the Mean
First, calculate the mean of the dataset by summing all the values and dividing by the total number of observations.

Mean = (12 + 31 + 42 + 36 + 41 + 32 + 41 + 71 + 10 + 11) / 10
Mean = 327 / 10
Mean = 32.7

Step 2: Calculate the Absolute Deviation
Next, calculate the absolute deviation of each data point from the mean by subtracting the mean from each value and taking the absolute value of the result.

Absolute Deviation from Mean:
|12 – 32.7| = 20.7
|31 – 32.7| = 1.7
|42 – 32.7| = 9.3
|36 – 32.7| = 3.3
|41 – 32.7| = 8.3
|32 – 32.7| = 0.7
|41 – 32.7| = 8.3
|71 – 32.7| = 38.3
|10 – 32.7| = 22.7
|11 – 32.7| = 21.7

Step 3: Calculate the Average Deviation
Finally, calculate the average deviation by averaging the absolute deviations calculated in the previous step.

Average Deviation = (20.7 + 1.7 + 9.3 + 3.3 + 8.3 + 0.7 + 8.3 + 38.3 + 22.7 + 21.7) / 10
Average Deviation = 155 / 10
Average Deviation = 15.5

3. Interpretation of Results

The average deviation for the given dataset is 15.5. This means that, on average, each data point in the dataset deviates from the mean by approximately 15.5 units. A higher average deviation indicates greater variability or dispersion of data points around the mean, while a lower average deviation suggests more consistency or uniformity in the dataset.

4. Conclusion

Average deviation is a measure of variability that quantifies the average distance of data points from the mean of the dataset. It provides insights into the dispersion of data around the central tendency. Calculating average deviation involves finding the absolute differences between each data point and the mean, then averaging these differences. In the case of the given dataset, the average deviation was found to be 15.5, indicating the average distance of data points from the mean.