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The following table gives the monthly income of 10 families in a town Family 12345678910 Monthly income (Rs.) 7800, 7600, 6900, 7500, 8400, 9200 ,11000, 8100, 10500, 9500 calculate the quartile deviation and its coefficient?
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The following table gives the monthly income of 10 families in a town ...
Calculation of Quartile Deviation and its Coefficient
Step 1: Arrange the Data in Ascending Order
- 6900
- 7500
- 7600
- 7800
- 8100
- 8400
- 9200
- 9500
- 10500
- 11000
Step 2: Calculate the Quartiles
- Q1 (First Quartile) = (n+1)/4 = (10+1)/4 = 2.75
- Q1 = 7500 + 0.75(7600-7500) = 7525
- Q2 (Second Quartile or Median) = (n+1)/2 = (10+1)/2 = 5.5
- Q2 = 8400
- Q3 (Third Quartile) = 3(n+1)/4 = 3(10+1)/4 = 8.25
- Q3 = 10075 + 0.25(10500-10075) = 10319
Step 3: Calculate the Quartile Deviation
- Quartile Deviation = (Q3-Q1)/2
- Quartile Deviation = (10319-7525)/2 = 1397
Step 4: Calculate the Quartile Deviation Coefficient
- Quartile Deviation Coefficient = (Quartile Deviation / (Q1+Q3)/2) x 100
- Quartile Deviation Coefficient = (1397 / (7525+10319)/2) x 100 = 13.33%
Explanation
The Quartile Deviation is a measure of variation which shows how spread out the data is. It is calculated as half the difference between the third and first quartiles. In this case, the Quartile Deviation is 1397.
The Quartile Deviation Coefficient is a measure of relative dispersion, which shows the Quartile Deviation as a percentage of the average of the first and third quartiles. In this case, the Quartile Deviation Coefficient is 13.33%, which means that the data is moderately dispersed.
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The following table gives the monthly income of 10 families in a town Family 12345678910 Monthly income (Rs.) 7800, 7600, 6900, 7500, 8400, 9200 ,11000, 8100, 10500, 9500 calculate the quartile deviation and its coefficient?
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The following table gives the monthly income of 10 families in a town Family 12345678910 Monthly income (Rs.) 7800, 7600, 6900, 7500, 8400, 9200 ,11000, 8100, 10500, 9500 calculate the quartile deviation and its coefficient? 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 following table gives the monthly income of 10 families in a town Family 12345678910 Monthly income (Rs.) 7800, 7600, 6900, 7500, 8400, 9200 ,11000, 8100, 10500, 9500 calculate the quartile deviation and its coefficient? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following table gives the monthly income of 10 families in a town Family 12345678910 Monthly income (Rs.) 7800, 7600, 6900, 7500, 8400, 9200 ,11000, 8100, 10500, 9500 calculate the quartile deviation and its coefficient?.
The following table gives the monthly income of 10 families in a town Family 12345678910 Monthly income (Rs.) 7800, 7600, 6900, 7500, 8400, 9200 ,11000, 8100, 10500, 9500 calculate the quartile deviation and its coefficient? 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 following table gives the monthly income of 10 families in a town Family 12345678910 Monthly income (Rs.) 7800, 7600, 6900, 7500, 8400, 9200 ,11000, 8100, 10500, 9500 calculate the quartile deviation and its coefficient? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following table gives the monthly income of 10 families in a town Family 12345678910 Monthly income (Rs.) 7800, 7600, 6900, 7500, 8400, 9200 ,11000, 8100, 10500, 9500 calculate the quartile deviation and its coefficient?.
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