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Assignment No: 1 (Lessons 19)
Question 1: Marks: 4+3=7
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.
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
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?
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CLASS BOUNDARIES:
117.5126.5
126.5135.5
135.5144.5
144.5153.5
153.5162.5
MIDPOINTS: (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 
118126  3  117.5126.5  3/34=0.08  3  117.5+126.5/2=122 
127135  5  126.5135.5  5/34=0.147  3+5=8  126.5+135.5/2=131 
136144  9  135.5144.5  9/34=0.264  8+9=17  135.5+144.5/2=140 
145153  12  144.5153.5  12/34=0.352  17+12=29  144.5+153.5/2=149 
154162  5  153.5162.5  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?
Answer: Nominal scale
Answer: Ordinal scale
Answer: Ratio scale
Answer: Interval scale
Yesrab Hussain
ID MC130202036
Assignment No: 1 (Lessons 19)
Question 1: Solution Marks: 4+3=7
Class limits 
Class Boundaries 
Frequency 
Relative Frequency 
Mid points 
Cumulative Frequency 
118126 
117.5126.5 
3 
3/34=0.088 
118+126/2=122 
3 
127135 
126.5135.5 
5 
5/34=0.147 
127+135/2=131 
3+5=8 
136144 
135.5144.5 
9 
9/34=0.264 
136+144/2=140 
3+5+9=17 
145153 
144.5153.5 
12 
12/34=0.353 
145+153/2=149 
3+5+9+12=29 
154162 
153.5162.5 
5 
5/34/0.147 
154+162/2=158 
3+5+9+12+5=34 
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
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?
STA301_Assignment#01_Solution_Spring_2013
see the attached file please
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/a_{1}+1/a_{2}+1/a_{3}+1/a_{4}+.......+1/a_{N})
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/a_{1}+1/a_{2}+1/a_{3}+1/a_{4}+.......+1/a_{N})
= 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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