FREQUENCY-DISTRIBUTIONS-AND-GRAPHS

FREQUENCY DISTRIBUTIONS AND GRAPHS

2-1 Organizing Data

RAW DATA

• When data are collected in original form
• When the raw data is organized into a frequency distribution, the frequency will be the number of values in a specific class of the distribution.

FREQUENCY DISTRIBUTION

• A frequency distribution is the organizing of raw data in table form, using classes and frequencies.

2-2 Three Types Of Frequency Distributions

CATEGORICAL FREQUENCY DISTRIBUTIONS

• can be used for data that can be placed in specific categories, such as nominal- or ordinal-level data.
• Examples - political affiliation, religious affiliation, blood type etc.

UNGROUPED FREQUENCY DISTRIBUTIONS

• can be used for data that can be enumerated and when the range of values in the data set is not large.
• Examples - number of miles your instructors have to travel from home to campus, number of girls in a 4-child family etc.

GROUPED FREQUENCY DISTRIBUTIONS

• can be used when the range of values in the data set is very large. The data must be grouped into classes that are more than one unit in width.
• Examples - the life of boat batteries in hours.

2-2 Terms Associated With A Grouped Frequency Distribution

CLASS LIMITS

• represent the smallest and largest data values that can be included in a class.
• In the lifetimes of boat batteries example, the values 24 and 30 of the first class are the class limits

LOWER LIMITS AND UPPER LIMITS

• The lower class limit is 24 and the upper class limit is 30.

CLASS BOUNDARIES

• are used to separate the classes so that there are no gaps in the frequency distribution.

CLASS WIDTH

• for a class in a frequency distribution is found by subtracting the lower (or upper) class limit of one class minus the lower (or upper) class limit of the previous class.

GUIDELINES FOR COMSTRICTING A FREQUENCY DISTRIBUTION

• There should be between 5 and 20 classes.
• The class width should be an odd number.
• The classes must be mutually exclusive.
• The classes must be continuous.
• The classes must be exhaustive.
• The class must be equal in width.

PROCEDURE FRO CONSTRUCTING A GROUPED FREQUENCY DISTRIBUTION

• Find the highest and lowest value.
• Find the range.
• Select the number of classes desired.
• Find the width by dividing the range by the number of classes and rounding up.
• Select a starting point (usually the lowest value); add the width to get the lower limits.
• Find the upper class limits.
• Find the boundaries.
• Tally the data, find the frequencies, and find the cumulative frequency.

GROUPED FREQUENCY DISTRIBUTION EXAMPLE

In a survey of 20 patients who smoked, the following data were obtained. Each value represents the number of cigarettes the patient smoked per day. Construct a frequency distribution using six classes.

• Step 1: Find the highest and lowest values: H = 22 and L = 5.
• Step 2: Find the range:
  R = H ^– L = 22 ^– 5 = 17.
• Step 3: Select the number of classes desired. In this case it is equal to 6.
• Step 4: Find the class width by dividing the range by the number of classes. Width = 17/6 = 2.83. This value is rounded up to 3.
• Step 5: Select a starting point for the lowest class limit. For convenience, this value is chosen to be 5, the smallest data value. The lower class limits will be 5, 8, 11, 14, 17, and 20.
• Step 6: The upper class limits will be 7, 10, 13, 16, 19, and 22. For example, the upper limit for the first class is computed as 8 - 1, etc.
• Step 7: Find the class boundaries by subtracting 0.5 from each lower class limit and adding 0.5 to the upper class limit.
• Step 8: Tally the data, write the numerical values for the tallies in the frequency column, and find the cumulative frequencies.

2-3 Histograms, Frequency Polygons, and Ogives

3 MOST COMMONLY USED GRAPHS IN RESEARCH

• Histogram.
• Frequency Polygon.
• Cumulative frequency graph, or ogive (pronounced o-jive).

HISTOGRAM

• is a graph that displays the data by using vertical bars of various heights to represent the frequencies.

FREQUENCY POLYGON

• is a graph that displays the data by using lines that connect points plotted for frequencies at the midpoint of classes. The frequencies represent the heights of the midpoints.

CUMULATIVE FREQUENCY GRAPH OR OGIVE

• is a graph that represents the cumulative frequencies for the classes in a frequency distribution.

OTHER TYPES OF GRAPHS

PARETO CHARTS

• is used to represent a frequency distribution for a categorical variable.

When constructing a Pareto chart

• Make the bars the same width.
• Arrange the data from largest to smallest according to frequencies.
• Make the units that are used for the frequency equal in size.

TIME SERIES GRAPH

• represents data that occur over a specific period of time.

PIE GRAPH

• is a circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution.