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The quartile deviation of a normal distribution with mean 10 and standard deviation 4 is?
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The quartile deviation of a normal distribution with mean 10 and stand...
Calculating Quartile Deviation of a Normal Distribution
Quartile deviation is a measure of dispersion which is defined as half of the difference between the third and first quartiles. It is also known as semi-interquartile range. The quartile deviation of a normal distribution with mean 10 and standard deviation 4 can be calculated as follows:
- Step 1: Calculate the first and third quartiles
- Step 2: Calculate the difference between the third and first quartile
- Step 3: Divide the difference by 2 to get the quartile deviation
Step 1: Calculate the first and third quartiles
The first quartile (Q1) is the 25th percentile and the third quartile (Q3) is the 75th percentile. For a normal distribution, we can use the standard normal distribution table to find the z-score for these percentiles.
- Q1 = z-score for the 25th percentile * standard deviation + mean
- Q3 = z-score for the 75th percentile * standard deviation + mean
Using the standard normal distribution table, we can find that the z-score for the 25th percentile is -0.67 and the z-score for the 75th percentile is 0.67.
- Q1 = -0.67 * 4 + 10 = 7.32
- Q3 = 0.67 * 4 + 10 = 12.68
Step 2: Calculate the difference between the third and first quartile
The difference between the third and first quartile is:
- Q3 - Q1 = 12.68 - 7.32 = 5.36
Step 3: Divide the difference by 2 to get the quartile deviation
The quartile deviation is:
- Quartile Deviation = (Q3 - Q1) / 2 = 5.36 / 2 = 2.68
Therefore, the quartile deviation of a normal distribution with mean 10 and standard deviation 4 is 2.68.
Community Answer
The quartile deviation of a normal distribution with mean 10 and stand...
Quartile deviation = 2/3 * standard deviation
= 2/3 * 4
= 2.675
= 2/3 * 4
= 2.675
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The quartile deviation of a normal distribution with mean 10 and standard deviation 4 is?
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The quartile deviation of a normal distribution with mean 10 and standard deviation 4 is? 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 The quartile deviation of a normal distribution with mean 10 and standard deviation 4 is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The quartile deviation of a normal distribution with mean 10 and standard deviation 4 is?.
The quartile deviation of a normal distribution with mean 10 and standard deviation 4 is? 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 The quartile deviation of a normal distribution with mean 10 and standard deviation 4 is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The quartile deviation of a normal distribution with mean 10 and standard deviation 4 is?.
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