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Objective(s) of this Assignment:

 

The assignment is being uploaded to build up the students concepts regarding:

 

  1. 1.   Measurement scale
  2. 2.   Stem and leaf
  3. 3.   Manipulation of data
  4. 4.   Measures of Central tendency

 

 

 

 

 

 

 

 

 

Assignment No: 1 (Lessons 1-9)

   Question 1:                                                                                                              Marks: 4+3=7

 

  1. Given the following frequency distribution:

     

Class Limits

Frequency

118 – 126

3

127 – 135

5

136 – 144

9

145 – 153

12

154 – 162

5

 

     Construct the columns of Class Boundaries, Relative Frequency, Mid points and

      Cumulative frequency.

  1. The ages of 22 patients admitted to a certain hospital during a particular week were as

follows:

66, 73, 68, 54, 25, 38, 67, 69, 74, 53, 52, 72, 55, 75, 37, 24, 13, 12, 11, 26, 39, 23

Construct a Stem and Leaf display for the above data. 

 

  Question 2:                                                                                                              Marks: 6+2=8

 

  1. Ten students (graduates and undergraduates) are enrolled in the course on statistics. Their weights are given below:

52, 63, 73, 58, 88, 72, 60, 76, 69, 74

Calculate Arithmetic mean, Geometric mean and Harmonic mean for the above data.

    b.    Which scale of measurement is more suitable in the following examples?

  • Religion can be categorized as Jewish, Muslim, Christian, Buddhist and “Other”.
  • A teacher ranks the students according to their oral language skills.
  • The number of minutes of overtime work that employees perform.
  • The number of questions asked by a customer during a simulated encounter with a salesperson.

  

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Replies to This Discussion

Q1: (a)
CLASS BOUNDARIES:
 117.5-126.5
 126.5-135.5
 135.5-144.5
 144.5-153.5
 153.5-162.5
MID-POINTS: (calculated by averaging the class limits)

 122
 131
 140
 149
 158
Relative frequency can be calculated by dividing frequency of each class
by the total frequency...
 In this question:
3/34= 0.088
5/34= 0.147
9/34= 0.264
12/34= 0.353
5/34= 0.147
CUMULATIVE FREQUENCY:
 3
 8
 17

 29
 34
(b):
Stem Leaf
1 1, 2, 3
2 3, 4, 5, 6
3 7, 8, 9
5 2, 3, 4, 5
6 6, 7, 8, 9
7 2, 3, 4, 5
Q2:(a)
 arithmetic mean = ぇX / n
arithmetic mean: 68.5
 Geometric Mean = ((X1)(X2)(X3)........(XN))1/N


geometric mean: 67.7

harmonic mean: 67.7
(b):
1. nominal
2. ordinal or ranking
3. interval
4. interval (please discuss this)



Geometric Mean :
Geometric Mean = ((X1)(X2)(X3)........(XN))1/N
where
X = Individual score
N = Sample size (Number of scores)



Geometric Mean Example: To find the Geometric Mean of 1,2,3,4,5.

Step 1: N = 5, the total number of values. Find 1/N.
1/N = 0.2

Step 2:Now find Geometric Mean using the formula.
((1)(2)(3)(4)(5))0.2 = (120)0.2
So, Geometric Mean = 2.60517


Harmonic Mean Formula :
Harmonic Mean = N/(1/a1+1/a2+1/a3+1/a4+.......+1/aN)
where
X = Individual score
N = Sample size (Number of scores)



Harmonic Mean Example: To find the Harmonic Mean of 1,2,3,4,5.

Step 1: Calculate the total number of values.
N = 5

Step 2: Now find Harmonic Mean using the above formula.
N/(1/a1+1/a2+1/a3+1/a4+.......+1/aN)
= 5/(1/1+1/2+1/3+1/4+1/5)
= 5/(1+0.5+0.33+0.25+0.2)
= 5/2.28
So, Harmonic Mean = 2.19


Q 2. b

1.. Nominal Scale
2.. Ordinal Scale
3.. Ratio Scale
4.. Interval Scale ( little confuse)
See page 4 in lecture 1

STA301 assignment 1 complete solution
STA301
Assignment no 1:



Question no 1:

a) Given the following frequency distribution construct the columns of class boundaries, relative frequency, mid points and cumulative frequency.

Solution:

Class limit Frequency Class boundaries Relative Frequency Cumulative Frequency Mid points
118-126 3 117.5-126.5 3/34=0.08 3 117.5+126.5/2=122
127-135 5 126.5-135.5 5/34=0.147 3+5=8 126.5+135.5/2=131
136-144 9 135.5-144.5 9/34=0.264 8+9=17 135.5+144.5/2=140
145-153 12 144.5-153.5 12/34=0.352 17+12=29 144.5+153.5/2=149
154-162 5 153.5-162.5 5/34=0.147 29+5=34 153.5+162.5/2=158

b) The ages of 22 patients admitted to a certain hospital during a particular week were as
Follows:
66, 73, 68, 54, 25, 38, 67, 69, 74, 53, 52, 72, 55, 75, 37, 24, 13, 12, 11, 26, 39, 23
Construct a Stem and Leaf display for the above data.






Solution:

Stem (Leading digit) Leaf (Trailing digit)
1 3 2 1
2 5 4 6 3
3 8 7 9
4 --------
5 4 3 2 5
6 6 8 7 9
7 3 4 2 5



Question no 2:

a) Ten students (graduates and undergraduates) are enrolled in the course on statistics. Their weights are given below:
52, 63, 73, 58, 88, 72, 60, 76, 69, 74
Calculate Arithmetic mean, Geometric mean and Harmonic mean for the above data.

Solution:

1: Arithmetic Mean

A.M. = sum of all observation / number of observations


=
=
= 68.5



2: Geometric Mean
G =
log G =
G = antilog
G =
By taking log on both sides:
Log G =
Log G = [1.7160+1.7993+1.8633+1.7634+1.9444+1.8573+1.7781+1 .8808+1.8388+1.8692]
Log G = *18.3106
Log G =
Log G = 1.83106
G = antilog 1.83106
G = 67.77



3: Harmonic Mean
H.M. =
H.M. =
H.M. =
H.M. =
H.M. = 67.613


b) Which scale of measurement is more suitable in the following examples?

  • Religion can be categorized as Jewish, Muslim, Christian, Buddhist and “Other”.


Answer: Nominal scale

  • A teacher ranks the students according to their oral language skills.


Answer: Ordinal scale

  • The number of minutes of overtime work that employees perform.


Answer: Ratio scale

  • The number of questions asked by a customer during a simulated encounter with a salesperson.


Answer: Interval scale

Assignment No.1 (Course STA301)

Spring 2013 (Total Marks 15)

Yesrab Hussain

ID MC130202036

                 Assignment No: 1 (Lessons 1-9)

   Question 1:   Solution                                                                                                 Marks: 4+3=7

 

  1. Given the following frequency distribution:

Class limits

Class Boundaries

Frequency

Relative Frequency

Mid points

Cumulative Frequency

118-126

117.5-126.5

3

3/34=0.088

118+126/2=122

3

127-135

126.5-135.5

5

5/34=0.147

127+135/2=131

3+5=8

136-144

135.5-144.5

9

9/34=0.264

136+144/2=140

3+5+9=17

145-153

144.5-153.5

12

12/34=0.353

145+153/2=149

3+5+9+12=29

154-162

153.5-162.5

5

5/34/0.147

154+162/2=158

3+5+9+12+5=34

 

  1. The ages of 22 patients admitted to a certain hospital during a particular week were as

follows:

66, 73, 68, 54, 25, 38, 67, 69, 74, 53, 52, 72, 55, 75, 37, 24, 13, 12, 11, 26, 39, 23

Construct a Stem and Leaf display for the above data. 

Stem

Leaf

1

1,2,3

2

3,4,5,6

3

7,8,9

5

2,3,4,5

6

6,7,8,9

7

2,3,4,5

 

 

 Question 2: solution                                                                                                         Marks: 6+2=8

 

  1. Ten students (graduates and undergraduates) are enrolled in the course on statistics. Their weights are given below:

52, 63, 73, 58, 88, 72, 60, 76, 69, 74

 

Arithmetic mean= sum of all the observation

                              Num of all the observation

Arithmetic mean=ΣX/n

 

X= 52+58+60+63+69+72+73+74+76+88/10

   =685/10=68.5Ans

           Geometric mean=log G= Σlogx/n

 

X

Log X

52

1.7160

58

1.7634

60

1.7781

63

1.7993

69

1.8388

72

1.8573

73

1.9633

74

1.8692

76

1.8808

88

1.9444

 

18.3106

 

           log G= Σlogx/n

        =18.3106/10

        =1.83106

G     = anti log 1.83106

        = 67.7 ans

 Harmonic mean

X

1/X

52

1/52=0.0192

58

1/58=0.0172

60

1/60=0.0166

63

1/63=0.0158

69

1/69=0.0145

72

1/72=0.0139

73

1/73=0.0137

74

1/74=0.0135

76

1/76=0.0132

88

1/88=0.0113

Σ1/x

0.1487

 

 

        H.M = n/ Σ1/x

       =10/0.1489 = 67.2 ans

 

 

 

    b.    Which scale of measurement is more suitable in the following examples?

  • Religion can be categorized as Jewish, Muslim, Christian, Buddhist and “Other”.(Nominal)
  • A teacher ranks the students according to their oral language skills.(ordinal or ranking)
  • The number of minutes of overtime work that employees perform.(ratio)
  • The number of questions asked by a customer during a simulated encounter with a salesperson.(interval)

  

STA301_Assignment#01_Solution_Spring_2013

see the attached file please

Attachments:

Geometric Mean Definition:
Geometric mean is a kind of average of a set of numbers that is different from the arithmetic average. The geometric mean is well defined only for sets of positive real numbers. This is calculated by multiplying all the numbers (call the number of numbers n), and taking the nth root of the total. A common example of where the geometric mean is the correct choice is when averaging growth rates.


Geometric Mean Example: To find the Geometric Mean of 1,2,3,4,5.

Step 1: N = 5, the total number of values. Find 1/N.
1/N = 0.2 

Step 2:Now find Geometric Mean using the formula.
((1)(2)(3)(4)(5))0.2 = (120)0.2 
So, Geometric Mean = 2.60517

This example will guide you to calculate the geometric mean manually.

Harmonic Mean Definition:
Harmonic mean is used to calculate the average of a set of numbers. Here the number of elements will be averaged and divided by the sum of the reciprocals of the elements. The Harmonic mean is always the lowest mean.

Harmonic Mean Formula :
Harmonic Mean = N/(1/a1+1/a2+1/a3+1/a4+.......+1/aN)
where 
X = Individual score 
N = Sample size (Number of scores)



Harmonic Mean Example: To find the Harmonic Mean of 1,2,3,4,5.

Step 1: Calculate the total number of values.
N = 5 

Step 2: Now find Harmonic Mean using the above formula.
N/(1/a1+1/a2+1/a3+1/a4+.......+1/aN)
= 5/(1/1+1/2+1/3+1/4+1/5)
= 5/(1+0.5+0.33+0.25+0.2)
= 5/2.28
So, Harmonic Mean = 2.19

This example will guide you to calculate the harmonic mean manually.

Arithmetic Median Definition:
Median is the middle value of the given numbers or distribution in their ascending order.Median is the average value of the two middle elements when the size of the distribution is even.

Example 1: To find the median of 4,5,7,2,1 [ODD].
Step 1: Count the total numbers given.
There are 5 elements or numbers in the distribution.

Step 2: Arrange the numbers in ascending order.
1,2,4,5,7

Step 3: The total elements in the distribution (5) is odd.
The middle position can be calculated using the formula. (n+1)/2 
So the middle position is (5+1)/2 = 6/2 = 3 
The number at 3rd position is = Median = 4

Example 2: To find the median of 4,5,7,2,1,8 [Even]
Step 1: Count the total numbers given.
There are 6 elements or numbers in the distribution.

Step 2: Arrange the numbers in ascending order.
1,2,4,5,7,8

Step 3: The total elements in the distribution (6) is even.
As the total is even, we have to take average of number at n/2 and (n/2)+1
So the position are n/2= 6/2 = 3 and 4 
The number at 3rd and 4th position are 4,5

Step 4: Find the median.
The average is (4+5)/2 = Median = 4.5


hope u will understand if any confusion dn ask...

Spring 2013_STA301_1_Solution

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