Stats 3 - Central Tendency and Spread

How is the mean calculated?

Sum of data points divided by total number of participants

Which measure of central tendency is used for reporting nominal variables?

Only mode because of the limited operationalization of nominal variables

Which measures of central tendency are used for reporting quantitative variables?

Mean, median, and mode because they are infinite and not limited

Variance

The variability that exists among participants’ scores on a given variable

Standard deviation

The typical (average) difference between the mean and a given data point

Difference/deviation scores

How far away a given data point is from the mean, always add up to 0

Sum of squares

All of the deviation scores squared and added up

Why is standard deviation the square root of the variance?

Brings the measure of spread back into the original units of the data, making it more intuitive and easier to interpret

Relationship among:  X —> M —> Deviation score  —> SS —> SD² —> SD

1. Sum of data points divided by total number of participants: M

2. X-M = deviation score, added up is 0

3. Square each deviation score individually

4. Sum of Squares is all of the squared deviation scores added up

5. Variance is SS divided by population N

6. Standard deviation is the square root of variance

7. Variance is the Standard deviation squared