Construct a frequency table and the Bar Chart.
frequency table
Ms.
Lubna Ineirat
# of decayed
teeth
Frequency(f)
Relative
frequency(r.f)
Cumulative
frequency(c.f)
total
32
Bar chart
Ms.
Lubna Ineirat
33
Example:
the following are ages of 25 college students
19, 18, 22, 20,20,
21, 23, 20,19,
22,20,
21, 20, 19,19, 21, 19, 20,
18, 20, 22, 19, 20, 21, 20
Construct the frequency table and bar chart.
frequency table
Ms.
Lubna Ineirat
Ages
Frequency
Relative
frequency
Cumulative
frequency
total
34
Bar chart
Ms.
Lubna Ineirat
35
The frequency distribution and graphic presentation
Frequency distribution:
is a grouping of data into mutually exclusion categories
showing the no of observations in each class.
Class :
is an
interval being with lower bound(L)and with upper
bound (U).
Class Mid Point(M.P):
Is a point divides a class into two equal part
C: (L, U)
M.P= ( L+M) / 2
ex : C : (1, 5)
M.P=
Class frequency (F):
The no. of observations in each class
Length of class(width):
obtained by subtract the lower limit of class from the next
lower class (the width classes is equal)
Relative frequency (r.f) =
frequency /n
Cumulative frequency:
it can
be computed by adding successive frequencies
Cumulative
relative frequency :
it can
be computed by adding successive
relative frequency
Ms.
Lubna Ineirat
36
Example:
the grades of 30 students
Frequency table
Ms.
Lubna Ineirat
Classes
Frequency
Mid Points
(M.P)
Relative
frequency
(r.f)
Cumulative
frequency
(c.f)
Cumulative
relative
frequency
(c.r.f)
1

5
6
6

10
9
11

15

20
3
Total
37
We can represent the above simple frequency table using the bar chart
Ms.
Lubna Ineirat
classes
frequency
Class
Boundaries
1

5
6
6

10
9
11

15
12
16

20
3
Total
30
38
Class frequency table
For large sample, we cant use the simple frequency table to represent the data
We need to divide the data into groups or intervals or classes
So
, we need to determine:
1 . The
number of intervals (K)
Too few intervals , are not good ,
too many, are not
because information will be lost.
helpful to summarize the data.
The formula to calculate K is
K=1+3.22 log(n)
Ms.
Lubna Ineirat
A commonly followed rule
is that
6
≤
K
≤
15
39
2. The Range (R)
It is the difference between the largest and the smallest observation in the data set.
3. The width
of the intervals (W)
Class intervals should be of the same width
Example:
Assume that the number
of observation equal 100 and the smallest
value =5, and the largest value= 61
Then
K=……
R=…..
W=……
Ms.
Lubna Ineirat
R
Range
W
K
#ofclasses
40
Histogram or Bar chart
Freq polygon
Ms.
Lubna Ineirat
41
Example:
the following data
are the grades of 40 students in a certain
exam. Construct a freqtable and the bar chart.
94, 82, 77, 75, 70, 62, 89, 57, 35, 92, 80, 85, 55, 45, 69, 75, 72, 90, 82, 62, 50,
44, 67, 53, 82, 90, 91, 82, 78, 62, 59, 81, 81, 55, 70, 80, 57, 47, 82, 70.
1.
Say the number of classes = 5 (given )
2.
Range = R = maxmin=
3.
Class width =W
Class
–
frequency table
Ms.
Lubna Ineirat
Class limits
frequency
Class marks
Class
boundaries
Total
42
Example:
a large internet
retailer that
sells medicine to pharmacies, is
studying the lead time
( elapsed time between when an order is placed and
when it is filled) for a sample of recent orders. The lead times are reported
in days.
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 Fall '19
 Standard Deviation, Ms. Lubna Ineirat