graphic representations in statistics

Graphical
Representations in
Statistics
BY UNSA SHAKIR

Why use charts and graphs?
– What do you lose?
–ability to examine numeric detail offered by a table
–potentially the ability to see additional relationships within the
data
–potentially time: often we get caught up in selecting colors and
formatting charts when a simply formatted table is sufficient
– What do you gain?
–ability to direct readers’ attention to one aspect of the evidence
–ability to reach readers who might otherwise be intimidated by
the same data in a tabular format
–ability to focus on bigger picture rather than perhaps minor
technical details

Statistics graph
Data recorded in surveys are displayed by a
statistical graph. There are some specific types of
graphs to study in the data statistics graphs.
There are eleven type of graphs used in Data
statistics graphs

Type of graphs
• Box plot,
• Stem and leaf plot,
• Frequency polygon,
• Scatter plot,
• Line graph,
• Bar graph,
• Histogram,
• Pictograph,
• Map chart,
• Pie chart,
• Line plot.

•A pictograph is used to represent tallies of categories.
• For example,
o categorical data might be seen in determining the month
that the most automobiles were sold.
o The month is the category. A symbol, or icon, is used to
represent a quantity of items.
Pictographs

Pictographs
•A symbol or an icon is used to represent a quantity of items.
A legend tells what the symbol represents.

Pictographs
•The number of students in each teacher’s fifth-grade class
at Hillview is depicted in tabular representation in the table
and in a pictograph.

•A dot plot, or line plot, provides a quick and simple way of
organizing numerical data.
•They are typically used when there is only one group of
data with fewer than 50 values.
Dot Plots

•Suppose the 30 students in Abel’s class received the
following test scores:
Dot Plots

•A dot plot for the class scores consists of a horizontal
number line on which each score is denoted by a dot, or an
x, above the corresponding number-line value. The number
of x’s above each score indicates how many times each
score occurred.
Dot Plots

The score 52 is
an outlier
Scores 97 and 98
form a cluster
A gap occurs
between scores 88
and 97.
Dot plots
Two students
scored 72.
Four students
scored 82.

Dot Plots
•If a dot plot is constructed on grid paper, then shading in
the squares with x’s and adding a vertical axis depicting the
scale allows the formation of a bar graph.

Stem and Leaf Plots
•The stem and leaf plot is similar to the dot plot, but the
number line is usually vertical, and digits are used rather
than x’s.
•In an ordered stem and leaf plot, the data are in order
from least to greatest on a given row.

Advantages of stem-and-leaf plots:
 They are easily created by hand.
 Do not become unmanageable when volume of data is
large.
 No data values are lost.
Disadvantage of stem-and-leaf plots:
 We lose information – we may know a data value exists,
but we cannot tell which one it is.
Stem and Leaf Plots

How to construct a stem-and-leaf plot:
1. Find the high and low values of the data.
2. Decide on the stems.
3. List the stems in a column from least to greatest.
4. Use each piece of data to create leaves to the right of
the stems on the appropriate rows.
Stem and Leaf Plots

5. If the plot is to be ordered, list the leaves in order from
least to greatest.
6. Add a legend identifying the values represented by
the stems and leaves.
7. Add a title explaining what the graph is about.
Stem and Leaf Plots

•Back-to-back stem-
and-leaf plots can be
used to compare two
sets of related data.
In this plot, there is
one stem and two sets
of leaves, one to the
left and one to the
right of the stem.
Back-to-Back Stem-and-Leaf Plots

graphic representations in statistics

Example
•Because the ages at death vary from 46 to 93, the stems
vary from 4 to 9. The first 19 presidents are listed on the left
and the remaining 19 on the right.

box plot
• Box plots (also called box-and-whisker plots or box-
whisker plots) give a good graphical image of the
concentration of the data.
• They also show how far the extreme values are from most
of the data.
• A box plot is constructed from five values: the minimum
value, the first quartile, the median, the third quartile, and
the maximum value.
• We use these values to compare how close other data
values are to them.

Step 1 – Order Numbers
1. Order the set of numbers from least to
greatest

2. Find the median. The median is the middle number. If
the data has two middle numbers, find the mean of
the two numbers. What is the median?
Step 2 – Find the Median

3. Find the lower and upper medians or quartiles.
These are the middle numbers on each side of the
median. What are they?
Step 3 – Upper & Lower Quartiles

Now you are ready to construct the actual box & whisker
graph. First you will need to draw an ordinary number
line that extends far enough in both directions to include
all the numbers in your data:
Step 4 – Draw a Number Line

Locate the main median 12 using a vertical
line just above your number line:
Step 5 – Draw the Parts

Locate the lower median 8.5 and the upper
median 14 with similar vertical lines:

• Next, draw a box using the lower and upper
median lines as endpoints:

Finally, the whiskers (small amount) extend out to
the data's smallest number 5 and largest number
20:

Step 6 - Label the Parts of a Box Plot
1 23
54
• Name the parts of a Box-Plot
Median Upper QuartileLower Quartile
Lower Extreme Upper Extreme

Interquartile Range
The interquartile range is the difference between
the upper quartile and the lower quartile.
14 – 8.5 =5.5

Example:
• Draw a box-and-whisker plot for the data set {3, 7, 8, 5,
12, 14, 21, 13, 18}.

Example:
• Suppose that the box-and-whisker plots below represent
quiz scores out of 25 points for Quiz 1 and Quiz 2 for the
same class. What do these box-and-whisker plots show
about how the class did on test #2 compared to test #1?

Frequency Tables
•A grouped frequency table shows how many times data
occurs in a range.
• The data for the ages
of the presidents at
death are
summarized in the
table.

 Each class interval has the same size.
 The size of each interval can be computed by subtracting
the lower endpoint from the higher and adding 1, e.g., 49
– 40 +1 = 10.
 We know how many data values occur within a particular
interval but we do not know the particular data values
themselves.
Frequency Tables
Characteristics of Frequency Tables

 As the interval size increases, information is lost.
 Classes (intervals) should not overlap.
Frequency Tables
Characteristics of Frequency Tables

Line graph:
• The line graph is used to plot the continuous data.
• The data's are plotted as points. The points are joined by
the lines.
• This graph is used to compare multiple data sets.

This is the symbolization of the line
graph.

Bar graph:
• The bar graph displays discrete data in disconnect
columns.
• A double bar graph can be used to evaluate two data
sets.
• It is visually muscular. It is used to easily evaluate two
or three data sets.

0
10
20
30
40
50
60
70
80
Living alone Married Other
Series1
N=13,886,000
Figure 3.3 Living Arrangements of Males (65 and Older) in the United States, 2000

• A double bar graph can be used to make
comparisons in data.
Double-Bar Graphs

0
10
20
30
40
50
60
70
80
Living alone Married Other
Males
Females
Figure 3.4 Living Arrangement of U.S. Elderly (65 and Older) by Gender, 2003

77.1
57.2
18
63.4
44.3
9.8
0 20 40 60 80 100
55 to 59
60- to 64
65 +
Women
Men
Figure 3.5 Percent of Men and Women 55 Years and Over in the Civilian Labor
Force, 2002

Other Bar Graphs
• The figure depicts a stacked bar graph.

pie chart:
• A graph showing the differences in frequencies or
percentages among categories of a nominal or an
ordinal variable.
• The categories are displayed as segments of a circle
whose pieces add up to 100 percent of the total
frequencies.
• The pie chart displays data as a percentage of the
whole. It displays the percentage of each category. But,
it has no exact data's.

White
Black
American Indian
Asian
Pacific Islander
Two or more
87.7%
8.3%
2.8%
.5%
.8% .6%
N = 35,919,174
Figure 3.1 Annual Estimates of U.S. Population 65 Years and Over by Race, 2003

Histogram:
• Histogram shows the differences in frequencies or
percentages among categories of an interval-ratio
variable.
• The histogram shows the continuous data in order to
columns.
• It is same as the line graph but it is represented as in
column format.
• A histogram is a special type of bar diagram.

0
5
10
15
20
25
30
65-69 70-74 75-79 80-84 85-89 90-94 95+
Figure 3.7 Age Distribution of U.S. Population 65 Years and Over, 2000

A frequency distribution table is
shown below
Class ( Cost of saree in
Rs.)
Frequency ( No. of
sarees sold in a week)
100 – 200 12
200 – 300 28
300 – 400 37
400 – 500 23
500 – 600 20
600 – 700 14
700 – 800 09

The Frequency Polygon
• A graph showing the differences in frequencies or
percentages among categories of an interval-ratio
variable.
• Points representing the frequencies of each category
are placed above the midpoint of the category and
are jointed by a straight line.

Figure 3.11. Population of Japan, Age 55 and Over, 2000, 2010, and 2020
Population of Japan, Age 55 and Over, 2000,
2010, and 2020
0
2,000,000
4,000,000
6,000,000
8,000,000
10,000,000
12,000,000
55-59 60-64 65-69 70-74 75-79 80+
2000
2010
2020
Source: Adapted from U.S. Bureau of the Census, Center for International Research,
International Data Base, 2003.

Time Series Charts
• A graph displaying changes in a variables at different
points in time.
• It shows time (measured in units such as years or
months) on the horizontal axis and the frequencies
(percentages or rates) of another variable on the
vertical axis.

Figure 3.12 Percentage of Total U. S. Population 65 Years and Over, 1900 to 2050
0
5
10
15
20
25
1900 1920 1940 1960 1980 2000 2020 2040 2060
Source: Federal Interagency Forum on Aging Related Statistics, Older Americans
2004: Key Indicators of Well Being, 2004.

Figure 3.13 Percentage Currently Divorced Among U.S. Population 65 Years and
Over, by Gender, 1960 to 2040
0
2
4
6
8
10
12
14
16
1960 1980 2000 2020 2040
Males
Females
Source: U.S. Bureau of the Census, “65+ in America,” Current Population Reports,
1996, Special Studies, P23-190, Table 6-1.

Scatter plot:
• The scatter pot shows the relationship between two
factors of the experiment.
• It displays the relationship between two data's.

This is the example of the scatter
plot.

The Statistical Map: The Geographic
Distribution of the Elderly
• We can display dramatic geographical changes in a
society by using a statistical map.
• Maps are especially useful for describing geographical
variations in variables, such as population distribution,
voting patterns, crimes rates, or labor force participation.

WHAT IS A CARTOGRAM?
• A cartogram is a colored map that gives a graphical
representation of statistical data.
• It is used for an immediate view of a phenomenon or
behavior.

Statistics in Practice
The following graphs are particularly suitable for making
comparisons among groups:
- Bar chart
- Frequency polygon
- Time series chart

graphic representations in statistics

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