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If mean 5 standard deviations =2.6 median =5 quartile deviation=1.5 then the coefficient of quartile deviation equals ?
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If mean 5 standard deviations =2.6 median =5 quartile deviation=1.5 th...
Calculating the Coefficient of Quartile Deviation
Given:
- Mean = 5 standard deviations = 2.6
- Median = 5
- Quartile deviation = 1.5
Step 1: Find the Value of the First Quartile (Q1)
The first quartile (Q1) is the value that separates the bottom 25% of the data from the top 75%. To find Q1, we can use the formula:
Q1 = median of the lower half of the data
Since the median is given as 5, we know that Q1 is the median of the values below 5. We don't have any specific values, but we know that the mean is 5 standard deviations, so:
Q1 = 5 - (5/2.6) = 3.846
Step 2: Find the Value of the Third Quartile (Q3)
The third quartile (Q3) is the value that separates the bottom 75% of the data from the top 25%. To find Q3, we can use the formula:
Q3 = median of the upper half of the data
Since the median is given as 5, we know that Q3 is the median of the values above 5. Again, we don't have any specific values, but we know that the mean is 5 standard deviations, so:
Q3 = 5 + (5/2.6) = 6.923
Step 3: Calculate the Interquartile Range (IQR)
The interquartile range (IQR) is the distance between Q1 and Q3:
IQR = Q3 - Q1 = 6.923 - 3.846 = 3.077
Step 4: Calculate the Coefficient of Quartile Deviation
The coefficient of quartile deviation (CQD) is defined as:
CQD = (IQR / median) x 100%
Plugging in the values we found:
CQD = (3.077 / 5) x 100% = 61.54%
Conclusion
The coefficient of quartile deviation for the given data is 61.54%. This indicates that the data is moderately dispersed around the median. A higher CQD value would indicate a greater degree of variability in the data.
Community Answer
If mean 5 standard deviations =2.6 median =5 quartile deviation=1.5 th...
Coefficient of quartile deviation= QD/Median×100
1.5/5×100 = 30
1.5/5×100 = 30
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If mean 5 standard deviations =2.6 median =5 quartile deviation=1.5 then the coefficient of quartile deviation equals ?
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If mean 5 standard deviations =2.6 median =5 quartile deviation=1.5 then the coefficient of quartile deviation equals ? 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 mean 5 standard deviations =2.6 median =5 quartile deviation=1.5 then the coefficient of quartile deviation equals ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If mean 5 standard deviations =2.6 median =5 quartile deviation=1.5 then the coefficient of quartile deviation equals ?.
If mean 5 standard deviations =2.6 median =5 quartile deviation=1.5 then the coefficient of quartile deviation equals ? 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 mean 5 standard deviations =2.6 median =5 quartile deviation=1.5 then the coefficient of quartile deviation equals ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If mean 5 standard deviations =2.6 median =5 quartile deviation=1.5 then the coefficient of quartile deviation equals ?.
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