Business Statistics: Summarizing Data

Summarizing Data

• Summarizing data graphically involves organizing raw data into mutually exclusive categories to show the number of observations in each class.

Frequency Distribution Table

• A frequency distribution table is a table that organizes raw data into mutually exclusive categories showing the number of observations in each class.
• Rules for constructing frequency distribution tables: • The table should have between 5 and 20 classes. • Classes must be mutually exclusive, continuous, and exhaustive. • Classes must be equal in width and size.

Definitions

• Class Limit: the starting and ending point of a particular class.
• Class Boundary: the midpoint between the upper class limit of a class and the lower class limit of the next class in sequence.
• Class Width/Size: the difference between the lower and upper class boundaries of a class interval.
• Class Midpoint: a point that divides a class into two equal parts.
• Class Frequency (f): the number of observations in each class.
• Relative Frequency (RF): the proportion of values falling into that class.
• Cumulative Frequency (CF): obtained by summing the frequency of a class and the frequencies of all the classes below it.

Constructing Grouped Frequency Distribution

• Steps for constructing grouped frequency distribution:
  1. Decide the number of classes using the formula 2k ≥ n, where k is the number of classes and n is the number of observations.
  2. Determine the class width using the formula w ≥ (H – L) / k, where H is the highest value and L is the lowest value.
  3. Set the individual class limits by starting from the lowest value in the data and adding the width to get the lower limit of the next class.
  4. Tally and record the number of items in each class.

Graphs for Quantitative Data

• Histogram: a graph that displays the data by using contiguous vertical bars of various heights to represent the frequencies of the classes.
• Cumulative Frequency Curve (Ogive): a graph that represents the cumulative frequencies for the classes in a frequency distribution.
• Scatter Plot: a graph that shows how one variable is affected by another.

Graphs for Categorical Data

• Bar Graph: a graph of vertical or horizontal bars whose heights represent the frequencies of respective categories.
• Pie Chart: a circle divided into sectors, where each sector represents a category of data and the area of each sector is proportional to the frequency of the category.