Standard deviation

Here are 3 concepts / steps that you will find useful when solving Standard Deviation Questions

Concept 1. How to compute Standard Deviation?
Step 1: Compute mean for the given set of numbers.
Step 2: Compute Deviation of each term from the mean. Deviation is computed by subtracting mean from each term. You will have as many deviations as the number of terms in the set.
Step 3: Square the deviations
Step 4: Compute the average of the squared deviations. This is the penultimate step. The result of this step is called Variance.
Step 5: Square root of Variance is the standard deviation.

Concept 2: If a constant 'k' is added or subtracted from each term in a set, the standard deviation does not change. Because, the relative difference between the numbers (and in turn the deviation from the mean) remain unchanged.

For example, let the original set comprise 3 numbers: 3, 4, 5. The mean is 4 and the deviations are -1, 0, and 1
Add 10 to each of the 3 terms, the revised numbers will be 13, 14, and 15. The mean is 15. But the deviations remain -1, 0, and 1

Concept 3: If a constant 'k' is multiplied to each term in a set, the standard deviation will become k times the initial SD. The relative difference between the numbers becomes k times the initial one.

For example, let the original set comprise 3 numbers: 3, 4, 5. The mean is 4 and the deviations are -1, 0, and 1
Multiply each element by 2. The revised numbers will be 6, 8, and 10. The new mean is 8. The deviations become -2, 0, and 2. So, the SD will change and the new SD will twice the old one.

A few questions may require you to compute SD. However, many questions will test whether you have understood what SD stands for (a measure of the extent of dispersion of data in a set) and will test application of concepts 2 and 3.

Cheers