PS296 Lecture Notes - Lecture 4: Linear Map, Standard Deviation, Random Variable
Transformations:
Linear transformation:
-calculation used to change from one scale of measurement to another
-applied to a random variable
-occurs by adding, subtracting, multiplying by or dividing by a constant
-converting feet to inches
-transformations change some properties of the distribution (centre and spread)
-but all the data within the distribution remain in the same location relative to each other
-the centre and spread of a distribution are affected differently by adding, subtracting,
multiplying and dividing by a constant
Addition and Subtraction:
-adding and subtracting by a constant affect the centre (mean and median, and mode)
-adding and subtracting by a constant however do not affect the variability (range,
variance, standard deviation)
-won't affect the overall state
-adding the same constant to each value increases the mean and median by that same
constant
-addition results in a horizontal shift to the right
Document Summary
Calculation used to change from one scale of measurement to another. Occurs by adding, subtracting, multiplying by or dividing by a constant. Transformations change some properties of the distribution (centre and spread) But all the data within the distribution remain in the same location relative to each other. The centre and spread of a distribution are affected differently by adding, subtracting, multiplying and dividing by a constant. Adding and subtracting by a constant affect the centre (mean and median, and mode) Adding and subtracting by a constant however do not affect the variability (range, variance, standard deviation) Adding the same constant to each value increases the mean and median by that same constant. Addition results in a horizontal shift to the right. Subtraction results in a horizontal shift to the left. Multiplying and dividing by a constant affect the centre (mean, median, and mode) and the variability.
