Statistics Class: Frequency Tables

Constructing a Frequency Table

• To construct a frequency table, first find the largest and smallest data values.
• Calculate the size of each class interval by dividing the range of data values by the number of classes.
• Determine the class intervals using the size of each class interval.
• Create the frequency table with columns for height (or other variable), frequency, lower limit, upper limit, midpoint, lower boundary, and upper boundary.

Calculating Midpoint, Lower Boundary, and Upper Boundary

• Midpoint = (lower limit + upper limit) / 2
• Lower boundary = lower limit - 0.5
• Upper boundary = upper limit + 0.5

Measures of Dispersion for Grouped Data

• Dispersion can be calculated using two methods.
• To compare the dispersions of two groups, calculate the range or interquartile range for each group.

Traffic Flow Survey

• The diagram shows the survey results of traffic flow in two different locations.
• The distribution shapes in both locations can be determined by examining the graph.
• The dispersions of car speeds in both locations can be compared by calculating the range or interquartile range.

Constructing an Ogive

• An ogive is a cumulative frequency graph.
• To construct an ogive, first create a frequency table with cumulative frequencies.
• Plot the cumulative frequencies against the upper boundaries of the class intervals.

Calculating Quartiles from an Ogive

• To find the first quartile (Q1), draw a horizontal line from the axis of cumulative frequency at 25% until it intersects the ogive, then draw a vertical line down to find the value of Q1.
• Repeat the process to find the second quartile (Q2) and third quartile (Q3).
• Interquartile range = Q3 - Q1.

Calculating Range

• Range = midpoint of the highest class - midpoint of the lowest class.
• Range can be used to measure the dispersion of a set of grouped data.

Construct a frequency table based on raw data, including finding the lower limit, upper limit, midpoint, lower boundary, and upper boundary. Learn how to organize data into classes and calculate class intervals.