2.2 Creating Frequency Distribution Theory

What is a frequency distribution?

(1) a list of values with corresponding frequencies

What are the 2 simple components of a frequency distribution table?

(1) classes (just groups)

(2) frequencies (just counts or tallies)

What are classes?

(1) just groups, ranges

What are frequencies?

(1) counts, tallies

(2) how something occurs frequently

What is a class width?

(1) the difference between two lower class limits

How do you solve for the class width?

What is the lower class limit?

(1) where the class starts, where the bound begins

(2) the smallest value belonging to a class

(3) the “left” value

What is the upper class limit?

(1) where the class ends, where the bound begins

(2) the largest value belonging to a class

(3) the “right” value

Steps to Setting Up a Frequency Distribution

Step 1: Determine number of classes

Step 2: Class width (rounded upwards)

Step 3: Make a table for the classes then frequencies

• Step 3.1: Lower class limits — determine the lower class limits by beginning with the lowest value and adding by the class width

• Step 3.2: Upper class limits — determine the upper class limits by subtracting 1 less from the consecutive lower class limit to figure out the “class range”

Step 4: Class midpoint — find the average of upper class limit and lower class limit, consequently figure out the succeeding values by adding the class width

Step 5: Class boundaries — the “midpoint” between one class to the next (usually involves a 0.5), the average of the upper class limit of the previous class and the lower class limit of the succeeding class. Don’t forget the class boundaries at the edges of the entire range (lowest value, subtract 0.5; highest value, add 0.5). For faster work, figure out the succeeding values by adding the class width

Step 6: Frequencies (count)

How do you solve for the class midpoint?

How do you solve for the class boundaries?

What is relative frequency distribution?

(1) compares the frequency of each class to the total number of data items you collected written as a percentage

Steps to Setting Up Relative Frequency Distribution

Step 1: Total frequency count, simply by adding all your frequencies

Step 2: Relative frequency percentage

Step 3: Create new column and fill out relative frequency

Relative Frequency Percentage Formula

What is cumulative frequency distribution?

(1) adding sequential classes together

(2) its like updating the balance every account as the table goes down

Steps to Finding the Cumulative Frequency Distribution

Step 1: Create new column: cumulative frequency distribution

Step 2: As you go down each row, add up everything before; like updating the balance each account

What does it mean when distribution is normal?

(1) when data rises to a peak and then falls down

What is a histogram?

(1) a touching bar chart

Steps to Creating a Histogram

Step 1: Create L-Chart

• Horizontal Axis: Classes

• Vertical Axis: Frequency

Step 2: Work on horizontal axis

• (1) Determine whether to use midpoints or boundaries, and plot equidistant points

  • Boundaries

    • Marks land on edges of each data, begins on the y-axis

  • Midpoints

    • Marks land at the center of each data, begins after the y-axis

• (2) Work faster by simply adding the class width after every each mark

Step 3: Work on vertical axis

• (1) Determine whether to use frequencies, relative frequencies, or cumulative frequencies

  • Frequencies

    • Plot the range of frequencies from lowest at the bottom to highest

  • Relative Frequencies

    • Plot the range (in percentage) of relative frequencies from lowest to highest

  • Cumulative Frequencies

    • Plot the range of cumulative frequencies from lowest to highest