STATISTICAL
CHARTS
Once data from a survey has been collected, it is
often displayed so that conclusions can be made
from it.
Raw data are often in the form of a tally chart
combined with a frequency table.
Frequency of any possible value is the number of times
it occurs in a survey.
Relative Frequency is the proportion of times that a
given value occurs in a survey.
Cumulative Frequency is found by successively adding
the frequencies
HST050 WK3LECT1 0 JPL
Displaying Quantitative Data
The commonly used graphs for
quantitative data are:
Bar Graph
 Histogram
The Cumulative frequency
graph OR Ogive curve.
Stem & Leaf Graph
HST050 WK3LECT1 0 JPL
Bar Graph
Bar Graphs are the most basic and useful visual
display of Discrete data (Grouped & Ungrouped
Data)
Drawn as follow
Discrete Grouped & Ungrouped Data
Frequency on vertical axis
Bars are separated
Bars are labeled
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Example-Ungrouped Data
Faculty
Frequency
Relative Frequency
FOA
FOBE
FOE
FONHS
FOS
TOTAL
6
10
7
9
8
40
0.15
0.25
0.175
0.225
0.20
1.00
Number of staff in each faculty that have already
receive the Covid19 vaccine
12
Frequency
10
8
6
4
2
0
FOA
FOBE
FOE
Faculty Name
HST050 WK3LECT1 0 JPL
FONHS
FOS
Example-Grouped Data
Age
Frequency
Relative Frequency
<17
17 - 19
20 - 22
23 - 25
>= 26
TOTAL
5
7
12
9
7
40
0.125
0.175
0.3
0.225
0.18
1.00
Age of students in Tutorial group A
14
12
Frequency
10
8
6
4
2
0
<17
17 - 19
20 - 22
Age
23 - 25
>= 26
Histogram
Histograms are the most basic and useful visual display
of continuous data. It displays the data by using
continuous vertical bars of various heights to represent
the frequency of the classes. The horizontal axis (x –
axis) represents the data (class boundaries) and the
vertical axis (y – axis) represents the frequency.
Bars on the histogram touch as the data is continuous
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Example
Height
150 - 155
155 - 160
160 - 165
165 - 170
170 - 175
175 - 180
180 - 185
Total
Frequency
2
3
5
11
4
3
2
30
Relative Frequency
0.07
0.10
0.17
0.37
0.13
0.10
0.07
1.00
Height of female students in HST050
12
Frequency
10
8
6
4
2
0
150 - 155
155 - 160
160 - 165
165 - 170
Height
170 - 175
175 - 180
180 - 185
Cumulative Frequency Graph (Ogive Curve)
The cumulative frequency is the sum of the
frequencies accumulated up to the upper
boundary of a class.
The Ogive curve is the graph that displays the
data by using lines that connect points plotted
for the cumulative frequencies and upper class
boundaries of the classes
HST050 WK3LECT1 0 JPL
Example
Construct an Ogive to represent the data shown
below for the weights of a group of 35 HST050
students
Basic Steps to Follow
1. Draw the x and y axis. Label x-axis with the class
boundaries. Use an appropriate scale for the y-axis to
represent the cumulative frequencies
2. Plot the upper class boundaries with the cumulative
frequencies
3. Connect adjacent points with line segments
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Ogive Curve
Weights of HST050 students
40
Cumulative Frequency
35
30
25
20
15
10
5
0
29.5
39.5
49.5
Weights
HST050 WK3LECT1 0 JPL
59.5
Cumulative Frequency Graphs
• With grouped discrete and grouped continuous
data, the cumulative frequency graph can be
used to estimate the median, quartiles, and
percentiles.
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Example: Find median and 80th percentile
Weights of HST050 students
Cumulative Frequency
40
35
30
25
20
15
10
5
0
29.5
39.5
44
49.5
52
59.5
Weights
Median =
𝟒𝟎
𝟐
= 𝟐𝟎th value ≈ 44
80th percentile = 40 × 80% = 32 ≈ 52.5
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Upper Quartile – 75%
Lower Quartile 25%
Stem and Leaf Graph
A stem and leaf diagram is used to organize data into
order as the data collected.
The first (and most significant) digits are placed in
advance on a vertical stem
Then, as the data is collected, the remaining
digit(s) are placed in a horizontal line (leaf) from
the stem
If the numbers on the stem are arranged in order,
the display can be viewed sideways to check for tge
underlying distribution of data – e.g. bell-shaped
for a normal distribution.
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Stem And Leaf Graph Example
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Stem And Leaf Graph Example
69
117
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2
5
10
15
17
25
25
28
29
32
33
42
2
29
32
42
15
25
10
17
5
33
25
28
First sort the data in ascending order
0
2
5
1
0
5
7
2
5
5
8
3
2
3
4
2
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9
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