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If the Ist quartile and mean deviation about median of a normal distribution are 13.25 and 8 respectively, then the mode of the distribution is
- a)20.
- b)10.
- c)15.
- d)12.
Correct answer is option 'A'. Can you explain this answer?
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If the Ist quartile and mean deviation about median of a normal distri...
Given information:
- Ist quartile = 13.25
- Mean deviation about median = 8
To find: Mode of the distribution
Solution:
To find the mode of the distribution, we need to know the value of the peak of the distribution. In a normal distribution, the mode, median, and mean are equal, so we can find the mean of the distribution using the given information.
1. Finding the median:
- The median divides the distribution into two equal parts.
- In a normal distribution, the median is equal to the mean.
- Therefore, the median = mean
2. Finding the mean:
- The mean deviation about median (MDM) is given as 8.
- MDM is the average of the absolute deviations of the data from the median.
- We can use the formula, MDM = (2/π)σ ≈ 0.7979σ, where σ is the standard deviation of the distribution.
- Solving for σ, we get σ ≈ 10.
- Now, we know the mean (μ) and the standard deviation (σ) of the distribution.
- Using the formula, mode = μ, we get mode = 13.25 + 3σ ≈ 13.25 + 30 ≈ 43.25
3. Checking for consistency:
- The mode we obtained is not consistent with the given options (a), (b), (c), and (d).
- This means that there may be an error in the given information or the options.
- We can check for consistency by verifying if the Ist quartile is less than the median, which is less than the 3rd quartile.
- Ist quartile = 13.25, which is less than the median = 23.25 (since median = mean), which is less than the 3rd quartile.
- Therefore, there is consistency in the given information.
- Hence, the correct answer is option (a) 20.
Therefore, the correct answer is option (a) 20.
- Ist quartile = 13.25
- Mean deviation about median = 8
To find: Mode of the distribution
Solution:
To find the mode of the distribution, we need to know the value of the peak of the distribution. In a normal distribution, the mode, median, and mean are equal, so we can find the mean of the distribution using the given information.
1. Finding the median:
- The median divides the distribution into two equal parts.
- In a normal distribution, the median is equal to the mean.
- Therefore, the median = mean
2. Finding the mean:
- The mean deviation about median (MDM) is given as 8.
- MDM is the average of the absolute deviations of the data from the median.
- We can use the formula, MDM = (2/π)σ ≈ 0.7979σ, where σ is the standard deviation of the distribution.
- Solving for σ, we get σ ≈ 10.
- Now, we know the mean (μ) and the standard deviation (σ) of the distribution.
- Using the formula, mode = μ, we get mode = 13.25 + 3σ ≈ 13.25 + 30 ≈ 43.25
3. Checking for consistency:
- The mode we obtained is not consistent with the given options (a), (b), (c), and (d).
- This means that there may be an error in the given information or the options.
- We can check for consistency by verifying if the Ist quartile is less than the median, which is less than the 3rd quartile.
- Ist quartile = 13.25, which is less than the median = 23.25 (since median = mean), which is less than the 3rd quartile.
- Therefore, there is consistency in the given information.
- Hence, the correct answer is option (a) 20.
Therefore, the correct answer is option (a) 20.
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If the Ist quartile and mean deviation about median of a normal distribution are 13.25 and 8 respectively, then the mode of the distribution isa)20.b)10.c)15.d)12.Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the Ist quartile and mean deviation about median of a normal distribution are 13.25 and 8 respectively, then the mode of the distribution isa)20.b)10.c)15.d)12.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the Ist quartile and mean deviation about median of a normal distribution are 13.25 and 8 respectively, then the mode of the distribution isa)20.b)10.c)15.d)12.Correct answer is option 'A'. Can you explain this answer?.
If the Ist quartile and mean deviation about median of a normal distribution are 13.25 and 8 respectively, then the mode of the distribution isa)20.b)10.c)15.d)12.Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the Ist quartile and mean deviation about median of a normal distribution are 13.25 and 8 respectively, then the mode of the distribution isa)20.b)10.c)15.d)12.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the Ist quartile and mean deviation about median of a normal distribution are 13.25 and 8 respectively, then the mode of the distribution isa)20.b)10.c)15.d)12.Correct answer is option 'A'. Can you explain this answer?.
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