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Assignment No: 1 (Lessons 1-9)
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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How to Calculate the Arithmetic Mean
A mathematical concept that usually is taught in elementary school, the arithmetic mean gives an average measurement for a given set of numbers. Being able to find a mean is very useful in everyday activities, such as figuring grades, setting a budget, calculating a business' financial output or determining an athlete's performance statistics.
Instructions
1
Write down the numbers for which you want to determine a mean. For instance, you might make a list of your electric bills for the past six months.
2
Add the numbers in the set that you wrote down in step one. For instance, you might add the following monetary values representing your electric bills:
120 + 150 + 135 + 100 + 90 + 125 = 720
3
Divide your answer from step two by the number of values in your set. Since you had six values in this set, you would perform the following equation to find the mean:
720 / 6 = 120.
Therefore, your average monthly electric bill would be 120 dollars.
Harmonic Mean
66, 73, 68, 54, 25, 38, 67, 69, 74, 53, 52, 72, 55, 75, 37, 24, 13, 12, 11, 26, 39, 23
Total Numbers: 22
Harmonic Mean: 32.24555
Q2
ANS:(b)
Nominal
Ordinal
Ratio
Ratio
may b wrong....
everyone, i m writting my answers here plz evaluate and discuss thx
Class boundries
117.5 - 126.5
----------
----------
153.5 - 162.5
Relative Frequency
0.088
----
---
0.147
Mid Pts
122
---
---
158
Q.2
Arithmetic Mean = 68.5
Geometric Mean = 67.78 and
Harmonic Mean = 67.02
Waiting for your reply please.
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
This example will guide you to calculate the geometric mean manually.
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.
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
CLASS BOUNDARIES:
117.5-126.5
126.5-135.5
135.5-144.5
144.5-153.5
153.5-162.5
RELATIVE FREQUENCY:
0.088
0.147
0.264
0.353
0.147
MID-POINTS:
122
131
140
149
158
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