Chapter 2: Organizing Data Section 2: Frequency Distribution and Histograms

Frequency Distribution Lists the number of occurrences for each category of data

Classes Categories of data created by using intervals of numbers Usually 5 to 15 classes.

Class Width The difference between consecutive lower class limits To find the class width… 1. largest data value – smallest data value desired number of classes 2. Increase result to next whole number

Class Limits The smallest value within the class. The largest value within the class.

Relative Frequency Distribution the relative frequency is listed, found by dividing the frequency (f) of each class by the sum of all the frequencies (n). class frequency (f) total of all frequencies (n)

Class Mark (Mid-Point) The number halfway between the lower and upper class limits of a class. To find the class mark… lower class limit + upper class limit 2

Graphic representations of (Grouped) Frequency Distributions Histogram- A type of bar graph. - Horizontal axis represents classes by labeling the class boundaries - vertical axis represents frequency or relative frequency - no space between bars  - bars must be the same width - width of bar represents a quantitative value, rather than a category

Class Boundary the halfway point between the upper limit of one class and the lower limit of the next class used as endpoints of the bars in a histogram

Three Classes Fr e q u e n c y

Histogram Examples (Cont). Five Classes frequency FFFFFFFFFFFF Ten Classes FFFFFFFFFFFFFF

Frequency Polygon type of line graph, horizontal axis labeled with class marks, vertical axis represents frequencies

Frequency Polygon

Relative frequency distribution for Scores on a Scientific Achievement Test LimitsTalliesFrequencyRelative Frequency 45-49II III IIIII I IIII IIIII IIII IIIII III III IIII I1

Relative frequency distribution for Scores on a Scientific Achievement Test LimitsTalliesFrequencyRelative Frequency 45-49II III IIIII I IIII IIIII IIII IIIII III III IIII I10.025

Uniform/Rectangular Distribution

Bell Shaped/Symmetrical Distribution

Skewed to the Left Distribution

Skewed to the Right Distribution