Frequency Distribution and
Graphs
JC T. Beringuel, MAEd., LPT, RECT, 4G1CJE
General Education/Electronics Engineering Department, College of Engineering
University of Rizal System - Morong Campus
Frequency Distribution
is a grouping of the data
into categories showing
the number of
observations in each of
the non-overlapping
classes.
Definition of Terms
Raw data- is the data collected in original form.
Range- is the difference of the highest value and the lowest
value in a distribution.
Class limits (or Apparent Limits)- is the highest and lowest
values describing a class.
Class Boundaries (or Real Limits)- is the upper and lower
values of a class for group frequency distribution whose values
has additional decimal place more than the class limits and
end with the digit 5.
Interval- is the distance between the class lower boundary and
the class upper boundary and it is denoted by the symbol i.
Definition of Terms (cont.)
Frequency- is the number of values in a specific class of a
frequency distribution.
Relative Frequency- is the value obtained when the frequencies in
each class of the frequency distribution is divided by the total
number of values.
Percentage- is obtained by multiplying the relative frequency by
100%.
Cumulative Frequency- is the sum of the frequencies
accumulated up to the upper boundary of a class in a frequency
distribution.
Midpoint- is the point halfway between the class limits of each
class and is representative of the data within that class.
Constructing Frequency Distribution
Grouped Frequency Distribution
- is used when the range of the
data set is larger; the data must
be grouped into classes whether
it is categorical data or interval
data.
A. Categorical Frequency
Distribution
B. Determining Class Interval
C. Grouped Frequency Distribution
Stem-and-Leaf Plot
A statistician named John
Turkey introduced the stemand-leaf plot. The objective
of this method is to some
extent overcomes the loss of
actual observations brought
about by the histogram.
The stem is the leading digit
or digits and the leaf is the
trailing digit. The stem is
places at the first column and
the leaf at the second column.
Graphical Frequency Distribution
A. Histogram - is a graph in which the
classes are marked on the horizontal
axis (x-axis) and the class frequencies
on the vertical axis (y-axis). The height
of the bars represents the class
frequencies, and the bars are drawn
adjacent to each other.
B. Frequency Polygon - is a graph that
displays the data using points which
are connected by lines. The
frequencies are represented by the
heights of the points at the midpoints
of the classes. The vertical axis
represents the frequency of the
distribution while the horizontal axis
represents the midpoint of the
frequency distribution.
Graphical Frequency Distribution (cont.)
C. Cumulative Frequency
Polygon (Ogive)- is a graph
that displays the
cumulative frequencies for
the classes in a frequency
distribution. The vertical
axis represents the
cumulative frequency of
the distribution while the
horizontal axis represents
the upper class boundaries
of the frequency
distribution.
Other Types of Graphs/ Charts
Pareto Chart- is a graph used to represent a frequency distribution
for a categorical data and frequencies are displayed by the heights
of vertical bars, which are arranged in order from highest to
lowest.
Bar Chart (Bar Graph)- is similar to bar histogram. The bases of
the rectangles are arbitrary intervals whose centers are the codes.
The height of each rectangle represents the frequency of that
category
Pie Chart (Circle Graph)- is a circle divided into portions that
represent the relative frequencies of the data belonging to different
categories. The data in a pie chart should be categorical or
nominal-level.
Pictograph (Pictogram)- it is immediately suggests the nature of
the data being shown. It is a combination of the attention-getting
quality and the accuracy of the bar chart. Appropriate pictures
arranged in a row present the quantities for comparison.