Upload
lilian-may-ando
View
1.084
Download
1
Tags:
Embed Size (px)
DESCRIPTION
:)
Citation preview
The More We Get Together
The more we get together, Together, together,
The more we get together, The happier we'll be.
For your friends are my friends,
And my friends are your friends.
The more we get together, The happier we'll be!
Graphical
Representation
Shapes of
Distribution
&
A graph adds life and beauty to one’s work, but more than this, it helps facilitate comparison and
interpretation without going through the numerical data.
Kinds of Graphs
Bar Chart
Histogram
Frequency Polygon
Pie Chart
Ogive
A bar chart is a graph represented by
either vertical or horizontal rectangles
whose bases represent the class intervals
and whose heights represent the
frequencies.
6
11
17
14
8
3
1 0
0
2
4
6
8
10
12
14
16
18
18-23 24-29 30-35 36-41 42-47 48-53 54-59 60- 65
fre
qu
en
cy
class interval
Bar Chart of the Grouped Frequency Distribution for the Entrance Examination Scores of 60
Students
A histogram is a graph represented by
vertical or horizontal rectangles whose
bases are the class marks and whose
heights are the frequencies.
0
2
4
6
8
10
12
14
16
18
20.5 26.5 32.5 38.5 44.5 50.5 56.5
Fre
qu
en
cy
class mark
The Histogram of the Grouped Frequency Distribution for the Entrance Examination Scores
of 60 Students
A frequency polygon is a line graph whose bases are the class marks and whose heights are the frequencies.
0 2 4 6 8
10 12 14 16 18
14.5 20.5 26.5 32.5 38.5 44.5 50.5 56.5 62.5
Fre
qu
en
cy
class mark
The Frequency Polygon of the Grouped Frequency Distribution for the Entrance Examination Scores of 60
Students
A pie chart is a circle graph showing the proportion of each class through either the relative or percentage frequency.
1.67% 10.00%
18.33%
28.33%
23.33%
13.33%
5.00%
The Pie Chart of the Grouped Frequency Distribution for the Entrance Examination
Scores of 60 Students
A pie chart is drawn by dividing the circle according to
the number of classes. The size of each piece depends
on the relative or percentage frequency distribution.
How to compute for the
Relative Frequency?
The relative frequency of each class is obtained by
dividing the class frequency by the total frequency.
Class
Interval
(ci)
Midpoint
(X)
Frequency
(f)
Relative
Frequency
(rf)
18 - 23 20.5 6 0.1000
24 - 29 26.5 11 0.1833
30 - 35 32.5 17 0.2833
36 - 41 38.5 14 0.2333
42 - 47 44.5 8 0.1333
48 - 53 50.5 3 0.0500
54 - 59 56.5 1 0.0167
N = 60
Relative Frequency Distribution for the Entrance Examination Scores of 60 Students
0
10
20
30
40
50
60
70
17.5 23.5 29.5 35.5 41.5 47.5 53.5 59.5
C
u
m
u
l
a
t
i
v
e
F
r
e
q
u
e
n
c
y
Class Boundaries
The Less than and Greater than Ogives for the Entrance Examination Scores of 60 Students
Less than ogive
Greater than ogive
An ogive is a line graph where the bases
are the class boundaries and the heights
are the <cf for the less than ogive and
>cf for the greater than ogive.
Shapes of
Distribution
Symmetrical
Asymmetrical
SYMMETRICAL
DISTRIBUTION
Normal Distribution
Each half or side of the
distribution is a mirror
image of the other side
(bell-shaped appearance)
Mean ,median ,and mode
coincides
(mean = median = mode)
Skewness is equal to
zero
ASYMMETRICAL
DISTRIBUTION
Negatively Skewed/Skewed
to the Left
In a negative skew the
tail extends far into the
negative side of the
Cartesian graph
mean < median
Skewness is less than 0.
the mass of the distribution
is concentrated on the right of
the figure
ASYMMETRICAL
DISTRIBUTION
Positively Skewed/Skewed to
the Right
In a positive skew the tail
on the right side of the
distribution exdends far
into the positive side of the
Cartesian graph.
mean > median
Skewness is greater than 0.
the mass of the distribution is
concentrated on the left of the
figure
Skewness refers to the degree of symmetry
or asymmetry of a distribution.
The extent of skewness can be obtained by
getting the coefficient of skewness using the
formula:
SK = 3(Mean – Median)
Standard deviation
Let us summarize the measurements from the 3 types of
distribution:
Normal Skewed to
the left/
Negatively
skewed
Skewed to
the right/
Positively
skewed
Mean 4.00 5.58 2.40
Median 4.00 6.00 2.00
Mode 4.00 6.00 2.00
Standard
deviation
1.53 1.07 1.07
Using the formula to find the coefficient
of skewness, we have:
For normal
distribution:
SK= 3(Mean – Median)
Standard deviation
= 3(4.0 – 4.0)
1.53
= 0
For skewed to the left
distribution:
SK= 3(Mean – Median)
Standard deviation
= 3(5.6 – 6.0)
1.07
= - 1.12
For skewed to the right
distribution:
SK= 3(Mean – Median)
Standard deviation
= 3(2.4 – 2.0)
1.07
= 1.12
Notice that if
•SK = 0, distribution is normal
•SK < 0, distribution is skewed to the left
•SK > 0, distribution is skewed to the right
Exercise
Find the coeff ic ient of skewness and indicate i f the
distr ibution is normal, skewed to the left or skewed to the
r ight.
72, 81, 67, 83, 61, 75, 78, 82, 71, 67
Solution:
Find the mean : Mean = 73.7
Find the median: Median = 73.5
Find the SD: SD = 7.38
Find the SK: SK = 3(Mean – Median)/Standard deviation
= 3(73.7 – 73.5)/ 7.38
= 0.08
Interpretation: Since SK is positive, then it is skewed to the
right. But the value is too small, so we can say that the
distribution is almost normal.
FIN
Reporters:
Ando, Lilian
Dillo, Charlyn
Lapos, Emilia