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Find the HM for the following data.
x : 2 4 8 16 20
y : 2 3 3 2 1
(a) 4.78 (b) 3.33 (c) 5.53 (d) none?
x : 2 4 8 16 20
y : 2 3 3 2 1
(a) 4.78 (b) 3.33 (c) 5.53 (d) none?
Most Upvoted Answer
Find the HM for the following data. x : 2 4 8 16 20 y : 2 3 3 2 1 (a) ...
Understanding Harmonic Mean (HM)
To find the Harmonic Mean for the given data, we first need to understand its formula. The Harmonic Mean is calculated as follows:
HM = n / (Σ(1/x))
where n is the number of observations, and Σ(1/x) is the sum of the reciprocals of the values.
Data Analysis
Given data:
- x: 2, 4, 8, 16, 20
- y: 2, 3, 3, 2, 1
For HM calculation, we will consider the values of x.
Steps to Calculate HM
1. Count of Observations (n):
- There are 5 observations (n = 5).
2. Calculate the Reciprocals:
- 1/2 = 0.5
- 1/4 = 0.25
- 1/8 = 0.125
- 1/16 = 0.0625
- 1/20 = 0.05
3. Sum of Reciprocals (Σ(1/x)):
- Σ(1/x) = 0.5 + 0.25 + 0.125 + 0.0625 + 0.05
- Σ(1/x) = 0.9875
4. Calculate HM:
- HM = 5 / 0.9875
- HM ≈ 5.06
Conclusion
The calculated Harmonic Mean is approximately 5.06. Thus, the closest answer from the options provided is:
- (d) none
This indicates that none of the options (a) 4.78, (b) 3.33, or (c) 5.53 match our calculated value.
To find the Harmonic Mean for the given data, we first need to understand its formula. The Harmonic Mean is calculated as follows:
HM = n / (Σ(1/x))
where n is the number of observations, and Σ(1/x) is the sum of the reciprocals of the values.
Data Analysis
Given data:
- x: 2, 4, 8, 16, 20
- y: 2, 3, 3, 2, 1
For HM calculation, we will consider the values of x.
Steps to Calculate HM
1. Count of Observations (n):
- There are 5 observations (n = 5).
2. Calculate the Reciprocals:
- 1/2 = 0.5
- 1/4 = 0.25
- 1/8 = 0.125
- 1/16 = 0.0625
- 1/20 = 0.05
3. Sum of Reciprocals (Σ(1/x)):
- Σ(1/x) = 0.5 + 0.25 + 0.125 + 0.0625 + 0.05
- Σ(1/x) = 0.9875
4. Calculate HM:
- HM = 5 / 0.9875
- HM ≈ 5.06
Conclusion
The calculated Harmonic Mean is approximately 5.06. Thus, the closest answer from the options provided is:
- (d) none
This indicates that none of the options (a) 4.78, (b) 3.33, or (c) 5.53 match our calculated value.
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Find the HM for the following data. x : 2 4 8 16 20 y : 2 3 3 2 1 (a) 4.78 (b) 3.33 (c) 5.53 (d) none?
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Find the HM for the following data. x : 2 4 8 16 20 y : 2 3 3 2 1 (a) 4.78 (b) 3.33 (c) 5.53 (d) none? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the HM for the following data. x : 2 4 8 16 20 y : 2 3 3 2 1 (a) 4.78 (b) 3.33 (c) 5.53 (d) none? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the HM for the following data. x : 2 4 8 16 20 y : 2 3 3 2 1 (a) 4.78 (b) 3.33 (c) 5.53 (d) none?.
Find the HM for the following data. x : 2 4 8 16 20 y : 2 3 3 2 1 (a) 4.78 (b) 3.33 (c) 5.53 (d) none? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the HM for the following data. x : 2 4 8 16 20 y : 2 3 3 2 1 (a) 4.78 (b) 3.33 (c) 5.53 (d) none? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the HM for the following data. x : 2 4 8 16 20 y : 2 3 3 2 1 (a) 4.78 (b) 3.33 (c) 5.53 (d) none?.
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