Frequency, Percentage, and Proportion

Statistical Symbols

• X or x = Individual Subject/value/score• N or n = Total number of

subjects/values/scores

Frequency Distributions

• an organization of raw data into tabular forms using categories/intervals and frequencies– frequency/frequency count• the # of times a specific value occurs in the data set

– often represented by the symbol f• 3 main types– categorical, ungrouped, & grouped

Frequency Distributions

• Categorical – AKA Qualitative Frequency Distribution• represents data that can be placed in specific

categories– Gender, Hair Color, Religious Affiliation

• Ex: AB B A O B

O B O A O

B O B B B

A O AB AB O

A B AB O A

Frequency Distributions

• Ex: Categorical Frequency Table

Category: Blood Type

Frequency f

A 5

B 8

O 8

AB 4

Total 25

Frequency Distributions

• Ungrouped – a simple listing of the data values w/ the f w/ which each

value occurs.

• Ex: Day 1 2 3 4 5 6 7 8 9 10

Defects 10 10 6 12 6 9 16 20 11 10

Day 11 12 13 14 15 16 17 18 19 20

Defects 11 11 9 12 11 7 10 11 14 21

Day 21 22 23 24 25

Defects 12 6 10 11 6

Frequency Distributions

• Ex: Ungrouped Frequency Table

Frequency Distributions

• Often times, the researcher will also display the relative frequency and the corresponding percentages – relative frequency for any value (class) • obtained by dividing the f for that class by the total

number of observations

Frequency Distributions• Ex: Ungrouped Frequency Table w/ Relative

Frequency and Percentage

Frequency Distributions

• Sometimes, the researcher will also display the cumulative frequencies and the cumulative relative frequencies– cumulative frequencies• for any specific value, the sum of the f for all values at

or below the given value

– cumulative relative frequencies • for any specific value, the sum of the relative

frequencies for all values at or below the given value

Frequency Distributions• Ex: Ungrouped Frequency Table w/ Cumulative

Frequency and Cumulative Relative Frequency

Frequency Distributions

• Grouped – obtained by constructing intervals of the values

for the data and then listing the corresponding f in each interval.

• Ex:

Frequency Distributions• Ex: Ungrouped Frequency Table w/ Cumulative

Frequency and Cumulative Relative Frequency