types of graphs and charts in statistics

1. TYPES OF CHARTS AND
GRAPH IN STATISTICS

2. What is Statistics??
• Statistics is the method of conducting a study
about a particular topic by collecting,
organizing, interpreting, and finally presenting
data.

3. Usage of statistics in our daily life
• Government Agencies
• Science and Medicine
• Psychology
• Education
• Companies

4. Definition of Bar Graph
 A Bar Graph is a chart that
uses either horizontal or vertical
bars to show comparisons
between categories

5. Classification of Bar Charts
Bar Charts
Single (vertical) Multiple Stacked

6. Y – Axis
Represents
individually separate
and distinct values.
X- Axis
Shows the specific
categories being
compared.

7. Advantages of Bar chart
• show each data category in a frequency
distribution
• display relative numbers or proportions of
multiple categories
• summarize a large data set in visual form
• estimate key values at a glance
• be easily understood due to widespread use in
business and the media

8. Disadvantages of Bar graph
• require additional explanation
• be easily manipulated to yield false
impressions
• fail to reveal key assumptions, causes, effects,
or patterns

9. Years 1989 1990 1991 1992 1993
Profit
(million $$)
10 12 18 25 42
EXAMPLE

10. Multiple Bar Chart

11. • A multiple bar chart is used to represent
distinct values for more than one item that
share the same category.

12. Example

13. SUBDIVIDED BAR GRAPH

14. SUBDIVIDED BAR GRAPH
• What is a sub divided bar graph?
Ans :- Sub-divided chat is used to represent data in which
the total magnitude is divided into different or
components.
• Why is subdivided bar graph used?
1. Sub-divided bar graph helpful in representing the total
number of elements in a group.
2. Sub-divided bar graph also helps in identifying and
comparing the difference between the components

15. EXAMPLE
DIVISION A B C
NUMBER OF BOYS 30 25 15
NUMBER OF GIRLS 15 20 35
TOTAL NUMBER OF
STUDENTS
45 45 50

16. GRAPH REPRESENTATION
0
10
20
30
40
50
60
A B C
Chart Title
NUMVBER OF BOYS NUMBER OF GIRLS

17. EXAMPLE
EXPENSE OF FAMILY A B
FOOD 2000 1700
CLOTHING 2400 2800
PETROL 1000 1100
TOTAL 5400 5600

18. GRAPH REPRESENTATION
2000 1700
2400
2800
1000 1100
0%
20%
40%
60%
80%
100%
A B
Chart Title
FOOD CLOTHING PETROL

19. HISTOGRAM

20. HISTOGRAM
• What is Histogram?
Ans :- Histogram is a graphical representation that is
helpful to organise and display the data in more
user-friendly format.
• Uses of Histogram
1. It helps in comparing process within specified
limits.
2. It summaries large data.
3. It assists in decision making.

21. EXAMPLE
CLASS
INTERVAL(PRICE
RANGE OF PENS)
20-30 30-40 40-50 50-60
FREQUENCY(NUMB
ER OF PENS)
15 20 30 25

22. GRAPH
0
5
10
15
20
25
30
35
20-30 30-40 40-50 50-60
FREQUENCY
20-30 30-40 40-50 50-60

23. EXAMPLE
• Let us take a large set of numbers :-
24, 17, 14, 22, 25, 26, 38, 42, 47, 24, 12, 28,
19, 32, 21, 46, 35, 28, 21, 31, 18, 19.
INTERVAL TALLY FREQUENCY
15-20 |||| 4
20-25 |||| 5
25-30 |||| 4
30-35 || 2
35-40 || 2
40-45 | 1
45-50 || 2

24. GRAPH
4
5
4
2 2
1
2
0
1
2
3
4
5
6
15-20 20-25 25-30 30-35 35-40 40-45 45-50
Series 1
15-20 20-25 25-30 30-35 35-40 40-45 45-50

25. FREQUENCY POLYGON

26. Frequency Polygon
• frequency polygon: graph that uses lines that connect
points plotted for the frequencies at the midpoints of the
classes; frequencies are represented by the heights of the
points
• To construct a frequency polygon:
– Find the midpoints of each class
– Draw the x and y axes. Label the x-axis with the midpoint of
each class then use a suitable scale for the frequencies on the y-
axis.
– Using the midpoints for the x values and the frequencies as the
y values, plot the points.
– Connect adjacent points with line segments. Draw a line back to
the x-axis at the beginning and end of the graph (where the next
midpoints would be located)

27. Frequency Polygon Example
Lower Limit Upper Limit Count Cumulative Count
29.5 39.5 0 0
39.5 49.5 3 3
49.5 59.5 10 13
59.5 69.5 53 66
69.5 79.5 107 173
79.5 89.5 147 320
89.5 99.5 130 450
99.5 109.5 78 528
109.5 119.5 59 587
119.5 129.5 36 623
129.5 139.5 11 634
139.5 149.5 6 640
149.5 159.5 1 641
159.5 169.5 1 642
169.5 179.5 0 642
A frequency polygon for 642 psychology test scores shown in Figure was constructed from the frequency table
. Frequency Distribution of Psychology Test Scores.

28. • The first label on the X-axis is 35. This represents an interval
extending from 29.5 to 39.5. Since the lowest test score is
46, this interval has a frequency of 0. The point labeled 45
represents the interval from 39.5 to 49.5. There are three
scores in this interval. There are 147 scores in the interval
that surrounds 85.
• You can easily discern the shape of the distribution from
Figure. Most of the scores are between 65 and 115. It is
clear that the distribution is not symmetric inasmuch as
good scores (to the right) trail off more gradually than poor
scores (to the left). In the terminology of Chapter 3 (where
we will study shapes of distributions more systematically),
the distribution is skewed.

30. OGIVES

31. The Ogive (Cumulative Frequency
Polygon)
• ogive: graph that represents the cumulative
frequencies for the classes in a frequency distribution
• To construct an ogive:
– Find the cumulative frequency for each class
– Draw the x and y axes. Label the x-axis with the class
boundaries. Label the y-axis with an appropriate frequency
(don’t use actual frequency numbers-yields uneven
intervals or classes)
– Plot the cumulative frequency at each upper class
boundary
– Starting with the first upper class boundary, connect
adjacent points with line segments. Extend the graph to
the first lower class boundary on the x-axis.

32. Constructing Statistical Graphs-
General Procedures
• Draw and label the x and y-axes
• Choose a suitable scale for the frequencies or
cumulative frequencies, and label it on the y-
axis.
• Represent the class boundaries for the
histogram or ogive, or the midpoint for the
frequency polygon, on the x-axis.
• Plot the points and then draw the bars or
lines.

33. Example
The following data consists of weights, in kilograms, of 20 people:
50, 65, 75, 80, 85, 85, 86, 86, 87, 87, 87, 90, 92, 98, 105.
Placing this data into a stem and leaf plot helps us organise and analyse and
group our data better. This is not a necessary step.
Step 1: Group your data into the table.
Stem Leaf
5 0
6 5
7 5
8 0, 5, 5, 6, 6, 7, 7, 7
9 0, 2, 8
10 5
Tally Frequency
Cumulative
Frequency
40<weights<50
50<weights<60
60<weights<70
70<weights<80
80<weights<90
90<weights<100
100<weights<110

34. Step 2: Put your data into the table
(Start with tallies)

35. Step 3: Put the frequencies by which
the events occurred

36. Step 4: Put in the cumulative frequency
totals

37. Step 5: Draw your graph
• The first coordinate in the plot always starts at a
• value of 0
• The second coordinate is at the end of the first interval.
• The third coordinate is at the end of the second interval and so on

38. PIE-CHART

39. Definition of Pie-Chart
• A pie chart (also called a Pie Graph or Circle
Graph) makes use of sectors in a circle. The
angle of a sector is proportional to the
frequency of the data.
• A pie chart is a good way of displaying data
when you want to show how something is
shared or divided.

40. The formula to determine the angle of
a sector in a circle graph is:
ANGLE OF SECTOR = FREQUENCY OF THE DATA
TOTAL FREQUENCY X 360

41. EXAMPLE
• In a school, there are 750 students in
Year1, 420 students in Year 2 and 630
students in Year 3. Draw a circle
graph to represent the numbers of
students in these groups.

42. SOLUTION
• Total number of students = 750 + 420 + 630 = 1,800.
Year 1 size of angle = X360 = 150o
Year 2 size of angle =
Year 3 size of angle =
420
1800 X360 =
630
1800
750
1800
X360 =
84o
126o
42%
23%
35%
No. of students
Year 1
Year 2
Year 3
150
360
X100 = 42%
84
360
X100 = 23%
X100 = 35%
126
360
So, In percentage =
So, In percentage =
So, In percentage =

43. Advantages
• Size of the circle can be made proportional to the
total quantity it represents
• Summarize a large data set in visual form
• Be visually simpler than other types of graphs
• Permit a visual check of the reasonableness or
accuracy of calculations
• Require minimal additional explanation
• Be easily understood due to widespread use in
business and the media

44. Disadvantages
• Do not easily reveal exact values.
• Many pie charts may be needed to show changes
over time
• Fail to reveal key assumptions, causes, effects, or
patterns
• Be easily manipulated to yield false impressions

45. PICTOGRAM

46. Definition of Pictogram
• Pictogram or pictograph represents the frequency of data as
pictures or symbols. Each picture or symbol may represent
one or more units of the data.

47. Example
• The following table shows the number of computers sold by a
company for the months January to March. Construct a
pictograph for the table.
Month Jan Feb Mar
No of
computers
25 35 20

48. Solution
January
February
March
Represents the 5 computers

49. Advantages
• Easy to read.
• Visually appealing.
Disadvantages
• They are difficult to draw
• Icons must be of consistent size.
• Best for only 2-6 categories.
• Very simplistic