Biostatistics, Chapter 2: Frequency Distributions and Graphs

Frequency Distribution

It is the organization of raw data in table form, using classes and frequencies. It is the most convenient method of organizing data.

Statistical charts and graphs

It is the most useful method of presenting the data.

Raw data

It is the data collected in its original form.

Frequency

It is the number of values in a specific class of the distribution.

1. Categorical Frequency Distribution

2. Grouped Frequency Distribution

2 types of Frequency Distribution

Categorical Frequency Distribution

It is used for data that can be placed in specific categories (nominal/ ordinal-level data).

Grouped Frequency Distribution

When the range of the data is large, the data must be grouped into classes that are more than one unit in width.

lower class limit

It represents the smallest data value that can be included in the class.

upper class limit

It represents the largest data value that can be included in the class.

class boundaries

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

gaps

due to the limits

class width

For a class in a frequency distribution, it is found by subtracting the lower (or upper) class limit of one class from the lower (or upper) class limit of the next class.

It will result in an incorrect answer.

Do not subtract the limits of a single class.

have enough classes

There should be between 5 and 20 classes.

to present a clear description of the collected data

The class width should be an odd number.

This ensures that the midpoint of each class has the same place value as the data.

class midpoint X

It is obtained by adding the lower and upper boundaries and dividing by 2, or adding the lower and upper limits and dividing by 2.

The classes must be mutually exclusive.

Mutually exclusive classes have non-overlapping class limits so that data cannot be placed into two classes.

The classes must be continuous.

Even if there are no values in a class, the class must be included in the frequency distribution. There should be no gaps in a frequency distribution.

The classes must be exhaustive.

There should be enough classes to accommodate all the data.

The classes must be equal in width.

This avoids a distorted view of the data.

open-ended distribution

It has no specific beginning value or no specific ending value.

ungrouped frequency distribution

When the range of the data values is relatively small, a frequency distribution can be constructed using single data values for each class.

to convey the data to the viewers in pictorial form

What is the purpose of graphs in statistics?

histogram 

It is a graph that displays the data by using contiguous vertical bars (unless the frequency of a class is 0) of various heights to represent the frequencies of the classes.

frequency polygon

It is a graph that displays the data by using lines that connect points plotted for the frequencies at the midpoints of the classes. The frequencies are represented by the heights of the points.

ogive

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

cumulative frequency

It is the sum of the frequencies accumulated up to the upper boundary of a class in the distribution.

relative frequency graphs

These distributions can be converted to distributions using proportions instead of raw data as frequencies.

distribution shapes

It determines the appropriate statistical methods used to analyze the data.

bell-shaped distribution

It has a single peak and tapers off at either end. It is approximately symmetric; i.e., it is roughly the same on both sides of a line running through the center.

uniform distribution

flat or rectangular.

J-shaped distribution

It has a few data values on the left side and increases as one moves to the right.

reverse J-shaped distribution

opposite of the J-shaped distribution.

right-skewed distribution

When the peak of a distribution is to the left and the data values taper off to the right.

left-skewed distribution

When the data values are clustered to the right and taper off to the left, a distribution is said to be.

unimodal

distributions with one peak.

bimodal

When a distribution has two peaks of the same height.

highest peak of a distribution

It indicates where the mode of the data values is.

mode 

It is the data value that occurs more often than any other data value.

pareto chart 

It is used to represent a frequency distribution for a categorical variable, and the frequencies are displayed by the heights of vertical bars, which are arranged in order from highest to lowest.

time series graph

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

pie graph

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

stem and leaf plot

It is a data plot that uses part of the data value as the stem and part of the data value as the leaf to form groups or classes.