Deviation in Values of Central Tendency

When we perform arithmetic operations (like adding, subtracting, multiplying, or dividing) on all values in a dataset, the measures of central tendency (mean, median, and mode) change in predictable ways.

Let's look at this with a simple dataset of test scores:

We have: Mean = , Mode = , (bimodal) and Median =

Now let's see what happens when we:

(1) Add 5 points to each score (additive transformation):

Mean = (increased by )

Mode = , (increased by )

Median = (increased by )

(2) Multiply each score by 1.5 (multiplicative transformation):

Mean = (original × )

Mode = , (original × )

Median = (original × )

Thus,

This concept is important because it helps us understand how data transformations affect our statistical measures, which is useful in data analysis, standardization, and scaling of data.