·
Axis: x
axis or ordinate

·
Axis: y axis or abscissa

·
Bar diagram, bar chart

·
Bar diagram, histogram

·
Class interval

·
Cumulative
frequency

·
Curve fitting

·
Data grouping

·
Data interpretation

·
Data tabulation

·
Data value

·
Diagram, line graph

·
Diagram, map

·
Diagram, pie chart

·
Diagram, scatter-gram

·
Diagram, stem and leaf

·
Frequency curves

·
Frequency
distribution

·
Frequency percent

·
Frequency
polygon

·
Frequency, relative frequency

·
Graph, smoothing of a graph

·
Graph, zero point of a graph

·
Grouping error

·
Kurtosis

·
Midpoint

·
Modality

·
Ogive

·
Origin of a graph

·
Score, grouped

·
Score, data value

·
Scores, raw

·
Shape of
distribution

·
Skewdness

UNIT OUTLINE

DATA GROUPING

A. Objective

B. Data Classes

C. Dichotomy/Trichotomy

D. Grouping Errors

DATA TABULATION

A. Objective

B. Type of Information Presented In Tables

C. Characteristics of an Ideal Table

D. Configurations of Tables

DATA DIAGRAMS SHOWING ONE QUANTITATIVE
VARIABLE

A. Characteristics of an Ideal Diagram

B. 1-Way Bar Diagrams: Bar Chart and Histogram

C. Stem and Leaf

D. Pie Chart

E. Map

** **

SHAPES OF DISTRIBUTIONS

A. Modality

B. Skewedness

C. Kurtosis

D. Common Shapes

E. Misleading Diagrams

UNIT SYNOPSIS

DATA GROUPING

Data grouping summarizes data but leads to loss of information due to grouping errors.
The suitable number of classes is 10-20. The bigger the class interval, the bigger the grouping error. Classes should be mutually
exclusive, of equal width, and cover all the data. The upper and lower class limits can be true or approximate. The approximate
limits are easier to tabulate. Data can be dichotomous (2 groups), trichotomous (3 groups) or polychotomous (>=3 groups).

DATA TABULATION

Tabulation summarizes data in logical groupings for easy visual inspection. A table shows
cell frequency (cell number), cell number as a percentage of the overall total (cell %), cell number as a row percentage (row
%), cell number as a column percentage (column %), cumulative frequency, cumulative frequency%, relative (proportional) frequency,
and relative frequency %. Ideal tables are simple, easy to read, correctly scaled, titled, labeled, self explanatory, with
marginal and overall totals. The commonest table is the 2 x 2 contingency table. Other configurations are the 2 x k table
and the r x c table.

DATA DIAGRAMS SHOWING ONE QUANTITATIVE VARIABLE

Diagrams present data visually. An ideal diagram is self-explanatory, simple, not crowded,
of appropriate size, and emphasizes data and not graphics. The 1-way bar diagram, the stem and leaf, the pie chart, and a
map are diagrams showing only 1 variable. A bar diagram uses ‘bars’ to
indicate frequency and is classified as a bar chart, a histogram, or a vertical line graph. The bar chart (with spaces
between bars) and the line graph (with vertical lines instead of bars) are used for discrete, nominal or ordinal data. The
histogram (with no spaces between bars) is used for continuous data. The area of the bar and not its height is proportional
to frequency. If the class intervals are equal, the height of the bar is proportional to frequency. The bar diagram is intuitive
for the non specialist. The stem and leaf diagram shows actual numerical values with the aid of a key and not their representation
as bars. It has equal class intervals, shows the shape of the distribution with easy identification of the minimum value,
maximum value, and modal class. The pie chart (pie diagram) shows relative
frequency % converted into angles of a circle (called sector angle). The area of each sector is proportional to the frequency.
Several pie charts make a doughnut chart. Values of one variable can be indicated
on a map by use of different shading, cross-hatching, dotting, and colors. A pictogram
shows pictures of the variable being measured as used instead of bars. A pictogram
shows pictures of the variable being measured as used instead of bars.

** **

SHAPES OF DISTRIBUTIONS

Bar diagrams and line graphs are distributions. The unimodal shape is the commonest shape. The 2 humps of the bimodal
need not be equal. More than 2 peaks are unusual. A perfectly symmetrical distribution is bell-shaped and is centered on the
mean. Skew to right (+ve skew) is more common than skew to the left (-ve skew). Leptokurtosis is a narrow sharp peak. Platykurtosis
is a wide flat hump. The common shapes are the normal, the s-curve (ogive), the reverse J-curve (exponential), and the uniform.
Diagrams can be misleading due to poor labeling, inappropriate scaling, omitting the zero origin, presence of outliers, and
presence of high leverage points, or using a wrong model (linear vs. quadratic). Widening and narrowing the scales produces
different impressions of the data. Double vertical scales can misleadingly be used to show spurious associations. Omitting
zero misleads unless broken line are used to show discontinuity.