The Effects Of Adding, Subtracting, Multiplying, And Dividing Data Points In A Distribution

Describe the effect of adding, subtracting, multiplying by, or dividing by a constant on the shape, center, and variability of a distribution of data.

Adding and subtracting does not affect shape, only where the shape is. Multiplying keeps the shape but it is more spread out. Dividing condenses the shape. Mean and median change from adding, subtracting, multiplying, and dividing. IQR, Range, and Standard Deviation change from multiplying and dividing only.

Adding a constant to every data point in a distribution will shift the entire distribution to the right/left without affecting its shape. In terms of center, the mean, median, and mode of the distribution will be shifted by the same constant. However, variance and standard deviation will remain the same.

Subtracting a constant from every data point in a distribution will shift the entire distribution to the left/right without affecting its shape. In terms of center, the mean, median, and mode of the distribution will be shifted by the same constant in the opposite direction. However, variance and standard deviation will remain the same.

Multiplying every data point in a distribution by a constant will stretch/shrink the distribution shape horizontally without affecting its center. In terms of center, the mean, median, and mode of the distribution will remain the same. However, variance and standard deviation will be multiplied by the square of the constant.

Dividing every data point in a distribution by a constant will shrink/stretch the distribution shape vertically without affecting its center. In terms of center, the mean, median, and mode of the distribution will remain the same. However, variance and standard deviation will be divided by the square of the constant. It’s important to note that dividing by a constant can result in outliers being heavily influenced by the division.

More Answers: