Section 2.1 Frequency Distribution & Their Graphs

Frequency Distribution

A table that shows classes or intervals of data with a count of the numbers of entries in each class

Frequency, f

The number of data entries within a class or interval

Lower class limit

The least number that can belong to a class

Upper class limit

The highest number that can belong to a class

Class Width

Is the distance between lower (or upper) limits of consecutive classes. Range divided by the number of classes

Range

The difference between the max & min data entries

Four basic steps to constructing a frequency distribution

1. Decide on the number of classes (5-20)

2. Find the class width by dividing the range by the number of classes

3. Find the class limits by adding the class width to consecutive lower class limits

4. Find the frequency by making a tally for each data entry in the row of the appropriate class

Midpoint Equation

(lower class limit + upper class limit) / 2

Relative Frequency Equation

class frequency / sample size

Cumulative Frequency

The sum of the frequency for that class and all the previous classes. When finished, should be equal to the sample size (n)

Frequency Histogram

A bar graph that represents the frequency distrubtion. The horizonal scale is quantitative and measures the data values. The vertical measures the frequencies. Consecutive bars touch and bars begin and end at class boundaries.

Frequency Polygon

A line graph that emphasizes the continuous change in frequencies. The graph begins and ends on the horizontal axis, so the left side is extened by one class width before the first class value. Same for the right side.

Relative Frequency Diagram

Same has the frequency histogram but the vertical axis measures the relative frequencies

Cumulative Frequency Graph/ Ogive

A line graph that displays the cumulative frequency of each class at its upper class boundary. The upper boundaries are marked on the horizontal axis and the cumulative frequencies on the vertical axis. Graph should end at the upper boundary of the last class