Scales of Measurement
What is a variable?
A variable is a value that we want to study
What is the formula for mean?
Sum of X / n
What is the relationship between standard deviation and variance?
SD is the square root of variance
Difference between sample and population?
Population: The group we are interested in.
Sample: A part of the population we study to understand the population.
If a distribution has an extreme outlier, which measure of central tendency should we not use?
Mean
What is the formula for Sum of Squares (definitional or computational)
SS=sum of (X-m)^2=sum of X^2- (sum of X)^2/n
Difference between ordinal and nominal scale?
Ordinal has ranking, nominal is just names
A sample of 15 scores has a mean of 10, we later found out that 1 of the scores was incorrect and should have been 7 instead of 17, what is the new mean?
(15*10-17+7)/15=9.333
Is it possible to have a distribution where SD =1, and range =10?
Yes
Which scale of measurement can be used for student’s midterm grades (Letter grades)?
Ordinal
If a distribution is positively skewed, what can we say about its mean and median?
Mean> median
Find the standard deviation for this population: 3, 3, 4, 5, 6, 6, 6
SS= (9+9+16+25+36+36+36)-(3+3+4+5+6+6+6)^2/7=167-155.57=11.43
sigma= sqrt(11.43/7)=1.278