The more we get together

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