Question

Background: Transformations with STATDISK

Math is a powerful tool that everyone should be good at, but when dealing with hundreds or thousands of data values math can be tedious at best. STATDISK offers data transformation functions to assist with that tedious math.

The "Sample Transformations" function is under the "Data" menu. The "Sample Transformer" window will open.This window allows for "Basic Transformations" and "Advanced Transformations." "Basic Transformation" allows users to add, subtract, multiply, or divide each value in a column by a constant. ;The results of that transformation appear in the right window pane. "Copy" these values into the appropriate column for later analysis within STATDISK.

Question:

Generate a new column of data using STATDISK for any of the data sets. Specifically, transform column 1 into column 2 by subtracting column 1 by 15. Which of the following statements are true?

Hint: There are three correct answers!

Group of answer choices

The mean of the transformed data is 15 more than the mean of the original data.

The median of the transformed data is the same as the median of the original data.

The mean of the transformed data is 15 less than the mean of the original data.

The median of the transformed data is 15 more than the median of the original data.

The standard deviation of the transformed data is 15 less than the standard deviation of the original data.

The median of the transformed data is 15 less than the median of the original data.

The standard deviation of the transformed data is 15 more than the standard deviation of the original data.

The mean of the transformed data is the same as the mean of the original data.

The standard deviation of the transformed data is the same as the standard deviation of the original data.

Answer 1

Solution

Back-up Theory

Change of Origin and Scale

Let x₁, x₂, x₃,…….. , x_n be a set on n observations.

Let y_i = x_i ± d; z_i = c.x_i; and w_i = c.x_i ± d; where c and d are constants.

The transformation from x to y is called Change of Origin.

The transformation from x to z is called Change of Scale.

The transformation from x to w is called Change of Origin and Scale.

Effect of Change of Origin and Scale on Various Statistical Measures.

A. Measures of Central Tendency

Any Measure of Central Tendency of y = Corresponding Measure of Central Tendency of x ± d. ……. (1a)

Any Measure of Central Tendency of z = c x Corresponding Measure of Central Tendency of x. ……. (1b)

Any Measure of Central Tendency of w = (c x Corresponding Measure of Central Tendency of x) ± d. (1c)

B. Measures of Dispersion

Any Measure of Dispersion of y = Corresponding Measure of Dispersion of x. ……............................ (2a)

Any Measure of Dispersion of z = c x Corresponding Measure of Dispersion of x. ….....................…. (2b)

Any Measure of Dispersion of w = c x Corresponding Measure of Dispersion of x. …....................…. (2c)

Now to work out the solution,

With the notation under Back-up Theory, ‘transform column 1 into column 2 by subtracting column 1 by 15’=> c = 0 and d = - 15.

Three correct answers are:

Vide (1a), The mean of the transformed data is 15 less than the mean of the original data. Answer 1

Vide (1a), The median of the transformed data is 15 less than the median of the original data. Answer 2

Vide (2a), Standard deviation of the transformed data is the same as the standard deviation of the original data. Answer 3

DONE