Descriptive Statistics: Measures of Central Tendency

Question 1

Central tendency

Answer 1

Measure used to determine a single score that best defines the center of a distribution (typical score)

Question 2

Choice of measure of central tendency depends on…

Answer 2

Shape of distribution, type of data, what you want to know, and sometimes convenience

Question 3

3 major groups of central tendency

Answer 3

Mean, median, and mode (but there are tons)

Question 4

Arithmetic mean

Answer 4

Sum of scores/number of scores

Question 5

Sample vs population mean

Answer 5

-Sample- sum of scores/sample = x bar
-Population- sum of scores/population = mu

Question 6

Qualities of arithmetic mean

Answer 6

-Every score in the distribution contributes to it
-Change, add, subtract a score —> change in the mean
-Add, subtract, multiple, divide every score by a constant —> doesn’t change overall shape, but changes the mean

Question 7

Median

Answer 7

Middle score that divides distribution in half so that 50% of scores fall above and 50% of scores fall below the median (50th percentile, 2nd quartile)

Question 8

Mode

Answer 8

Score/category with greatest frequency

Question 9

When is mean preferred?

Answer 9

-In most cases
-Typically provides a representative value for the set
-Every score contributes to calculation

Question 10

Mean limitations

Answer 10

-Easily influenced by extreme scores
-Value may not actually exist as an observed score, not intuitive

Question 11

When is median preferred?

Answer 11

When the data is skewed or contains extreme values

Question 12

When is mode preferred?

Answer 12

-Nominal data (category)
-Discrete and ordinal data when interpretation lies on whole numbers (how many times have you cheated on your partner?)

Question 13

Example of central tendency in your everyday life

Answer 13

-Calculating the mean salary of employees in a company to understand the typical level of pay
-Calculating the mean on an exam to get a representation of how the class did