in days.
Construct a frequency histogram?
Ms.
Lubna Ineirat
Lead Time
(days)
Frequency
1 up to 5
6
5 up to 9
7
9 up to A
11
13 up to 17
B
17 up to 21
7
Total
40
43
Age Group (in
years)
Frequency
Relative frequency
Cumulative
frequency
5

14
6
0.08
6
15

24
A
C
15
25

34
B
0.24
E
G

44
24
D
57
45

54
15
0.20
F
55

H
3
0.04
75
Ms.
Lubna Ineirat
Example:
the following information has been collected from 75 patients
who visited the diabetic clinic in Ramallah. Complete the table .
44
Homework
: Complete the following table:
Ms.
Lubna Ineirat
45
class
Frequency
Relative frequency
8

10
2
F
A
4
0.2
14

16
C
G
17

M
D
0.4
B
I
H
Total
E
1
Summary Descriptive Measures
measures of central Tendency
measures of variability
measures of central Tendency(Mean / median
/mode )
1. Mean
Population mean
μ
=
,
N is population size.
Sample mean
, n is sample size.
Example
:
evaluate
x
a.
3, 4, 5, 3, 2
b.
3, 4, 5, 3, 2, 20
c.
3, 4,
5, 3, 2, 10
Ms.
Lubna Ineirat
46
X
i
x
n
x
i
N
Note:
Mean for frequency table
Homework
: evaluate x
Ms.
Lubna Ineirat
47
Mark
Frequency
90
1
85
3
80
2
70
4
Total
# of decayed teeth
Frequency
0
1
1
2
2
4
3
5
4
2
5
2
Total
Example
: Find (Approximate
x)
Homework: the following information has been collected from a
sample of 25 children who visited the diabetic clinic in Jenin:
Ms.
Lubna Ineirat
48
grades
Frequency
1

5
6
6

10
9
11

15
12
16

20
3
Total
Example
: the following information has been collected from a sample of 25 children who visited the
diabetic clinic .
1.
Estimate the sample mean.
2.
What is the percentage of the children who weighs more than 15 kgs?
3.
What is the percentage of the children who weighs up to 11 kgs?
4.
Estimate the mean weight in the third
class?
5.
What is the approximate number in the second class?
Ms.
Lubna Ineirat
49
Weight in (kgs)
Frequency
4

7
2
8

11
8
12

15
11
16

19
4
Total
Homework
: fill in the blank the following table:
1.
Estimate the sample mean.
2.
What is the percentage of the data more than 5 kgs?
3.
What is the percentage of the data less than
8
kgs?
4.
Estimate the mean in the second
class?
5.
What is the approximate number of he
fourth class?
Ms.
Lubna Ineirat
50
classes
Frequency
2

4
1
5

A
C
8

10
8
11

B
3
Total
15
Homework:
consider the following frequency table that represents marks for students.
a.
Find the mean
?
b.
Find the standard deviation?
c.
What is the approximate number
in the second class?
d.
Estimate the total Marks in the forth class?
e.
What is the expected Mark for a students in the interval 1620?
Ms.
Lubna Ineirat
51
Grades
Frequency
 10
2
11 
15
5
16

20
7

Total
10
Mode
: the observation with largest frequency
Example
:
find the mode for the following data
a.
1, 2, 4, 5 ,4 ,6 ,2.
b.
2, 2, 4, 4, 5, 5, 6, 6, 8, 8.
c.
1, 2, 3, 3, 2, 3, 5, 6, 7
Ms.
Lubna Ineirat
52
Median(Md)
: is the value that divides the data set into two equal parts.
First step to find the
median
is to
Order
the data from smallest to largest value
Example
:
find the median for the following data
1.
3 , 5, 7, 8, 10, 15
2.
21, 19, 23, 25, 18, 9, 7,9,22
3.
35, 47, 48, 50, 53, 57,61, 70, 72, 80
Ms.
Lubna Ineirat
53
Example
:
find the median
Ms.
Lubna Ineirat
54
Note:
Measure of Variability ( range / variance / standard deviation)
Range = max
–
min .
You've reached the end of your free preview.
Want to read all 70 pages?
 Fall '19
 Standard Deviation, Ms. Lubna Ineirat