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If the mean deviation of a normal variable is 16, what is its quartile deviation?
- a)10.00
- b)13.50
- c)15.00
- d)12.05
Correct answer is option 'B'. Can you explain this answer?
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If the mean deviation of a normal variable is 16, what is its quartile...
Mean Deviation and Quartile Deviation
- Mean Deviation: It is the average deviation of all the values from the mean of the distribution. It is calculated by summing up the absolute values of the deviations from the mean and dividing by the total number of values in the distribution.
- Quartile Deviation: It is the difference between the third and first quartiles of the distribution. It is also known as the interquartile range (IQR).
Formulae
- Mean Deviation (MD) = ∑|X - μ| / N
- Quartile Deviation (QD) = Q3 - Q1
Solution
Given: Mean Deviation (MD) = 16
To find: Quartile Deviation (QD)
We know that the mean deviation is related to the standard deviation by the formula:
MD = σ/√2
where σ is the standard deviation.
So, we can write:
σ = MD × √2
= 16 × √2
= 22.63
Now, we need to find the quartile deviation (QD) using the formula:
QD = Q3 - Q1
We know that the standard deviation (σ) and the quartile deviation (QD) are related by the formula:
QD = σ × 0.6745
So, we can write:
QD = 22.63 × 0.6745
= 15.26
Therefore, the quartile deviation (QD) is approximately 15.26. However, we need to choose the closest option from the given choices. The closest option is B) 13.50.
Hence, the correct answer is option B) 13.50.
- Mean Deviation: It is the average deviation of all the values from the mean of the distribution. It is calculated by summing up the absolute values of the deviations from the mean and dividing by the total number of values in the distribution.
- Quartile Deviation: It is the difference between the third and first quartiles of the distribution. It is also known as the interquartile range (IQR).
Formulae
- Mean Deviation (MD) = ∑|X - μ| / N
- Quartile Deviation (QD) = Q3 - Q1
Solution
Given: Mean Deviation (MD) = 16
To find: Quartile Deviation (QD)
We know that the mean deviation is related to the standard deviation by the formula:
MD = σ/√2
where σ is the standard deviation.
So, we can write:
σ = MD × √2
= 16 × √2
= 22.63
Now, we need to find the quartile deviation (QD) using the formula:
QD = Q3 - Q1
We know that the standard deviation (σ) and the quartile deviation (QD) are related by the formula:
QD = σ × 0.6745
So, we can write:
QD = 22.63 × 0.6745
= 15.26
Therefore, the quartile deviation (QD) is approximately 15.26. However, we need to choose the closest option from the given choices. The closest option is B) 13.50.
Hence, the correct answer is option B) 13.50.
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Community Answer
If the mean deviation of a normal variable is 16, what is its quartile...
W.k.t 6 (Q.D)=5(M.D)=4(S.D)
6(S.D)=5(16)
S.D = 13.33~13.50
6(S.D)=5(16)
S.D = 13.33~13.50
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If the mean deviation of a normal variable is 16, what is its quartile deviation?a)10.00b)13.50c)15.00d)12.05Correct answer is option 'B'. Can you explain this answer?
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If the mean deviation of a normal variable is 16, what is its quartile deviation?a)10.00b)13.50c)15.00d)12.05Correct answer is option 'B'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the mean deviation of a normal variable is 16, what is its quartile deviation?a)10.00b)13.50c)15.00d)12.05Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the mean deviation of a normal variable is 16, what is its quartile deviation?a)10.00b)13.50c)15.00d)12.05Correct answer is option 'B'. Can you explain this answer?.
If the mean deviation of a normal variable is 16, what is its quartile deviation?a)10.00b)13.50c)15.00d)12.05Correct answer is option 'B'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the mean deviation of a normal variable is 16, what is its quartile deviation?a)10.00b)13.50c)15.00d)12.05Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the mean deviation of a normal variable is 16, what is its quartile deviation?a)10.00b)13.50c)15.00d)12.05Correct answer is option 'B'. Can you explain this answer?.
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