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Continuous series Calculate quartile deviation and the coefficient of quartile deviation from the following data.Wages in rupees per day lesser than 35-37 38-40 41-43 over 43Number of wages 14 62 99 18 7
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Continuous series Calculate quartile deviation and the coefficient of ...
To calculate quartile deviation, we first need to find the first and third quartiles.
Step 1: Find the total number of wages:
Total number of wages = 14 + 62 + 99 + 18 + 7 = 200
Step 2: Find the cumulative frequency for each class interval:
Class interval | Lesser than | Cumulative frequency
-------------------------|-------------|----------------------
35-37 | 14 | 14
38-40 | 62 | 76
41-43 | 99 | 175
Over 43 | 18 | 193
Total | | 200
Step 3: Calculate the first quartile (Q1):
Q1 = L + [(N/4 - CF) / f] x i
where,
L = lower limit of the median class
N = total number of observations
CF = cumulative frequency of the class before the median class
f = frequency of the median class
i = width of the class interval
For Q1, N/4 = 200/4 = 50
The median class is 38-40, with a cumulative frequency of 76.
L = 37 (lower limit of the median class)
CF = 14 (cumulative frequency of the class before the median class)
f = 62 (frequency of the median class)
i = 3 (width of the class interval)
Q1 = 37 + [(50 - 14) / 62] x 3 = 37 + (36/62) x 3 = 38.6
Step 4: Calculate the third quartile (Q3):
Q3 = L + [(3N/4 - CF) / f] x i
For Q3, 3N/4 = 3 x 200/4 = 150
The median class is 41-43, with a cumulative frequency of 175.
L = 40 (lower limit of the median class)
CF = 76 (cumulative frequency of the class before the median class)
f = 99 (frequency of the median class)
i = 3 (width of the class interval)
Q3 = 40 + [(150 - 76) / 99] x 3 = 40 + (74/99) x 3 = 42.3
Step 5: Calculate quartile deviation:
Quartile deviation = (Q3 - Q1) / 2
Quartile deviation = (42.3 - 38.6) / 2 = 1.85
Step 6: Calculate coefficient of quartile deviation:
Coefficient of quartile deviation = (Quartile deviation / (Q3 + Q1) / 2) x 100
Coefficient of quartile deviation = (1.85 / (42.3 + 38.6) / 2) x 100 = 5.68%
Therefore, the quartile deviation is 1.85 and the coefficient of quartile deviation is 5.68%.
Step 1: Find the total number of wages:
Total number of wages = 14 + 62 + 99 + 18 + 7 = 200
Step 2: Find the cumulative frequency for each class interval:
Class interval | Lesser than | Cumulative frequency
-------------------------|-------------|----------------------
35-37 | 14 | 14
38-40 | 62 | 76
41-43 | 99 | 175
Over 43 | 18 | 193
Total | | 200
Step 3: Calculate the first quartile (Q1):
Q1 = L + [(N/4 - CF) / f] x i
where,
L = lower limit of the median class
N = total number of observations
CF = cumulative frequency of the class before the median class
f = frequency of the median class
i = width of the class interval
For Q1, N/4 = 200/4 = 50
The median class is 38-40, with a cumulative frequency of 76.
L = 37 (lower limit of the median class)
CF = 14 (cumulative frequency of the class before the median class)
f = 62 (frequency of the median class)
i = 3 (width of the class interval)
Q1 = 37 + [(50 - 14) / 62] x 3 = 37 + (36/62) x 3 = 38.6
Step 4: Calculate the third quartile (Q3):
Q3 = L + [(3N/4 - CF) / f] x i
For Q3, 3N/4 = 3 x 200/4 = 150
The median class is 41-43, with a cumulative frequency of 175.
L = 40 (lower limit of the median class)
CF = 76 (cumulative frequency of the class before the median class)
f = 99 (frequency of the median class)
i = 3 (width of the class interval)
Q3 = 40 + [(150 - 76) / 99] x 3 = 40 + (74/99) x 3 = 42.3
Step 5: Calculate quartile deviation:
Quartile deviation = (Q3 - Q1) / 2
Quartile deviation = (42.3 - 38.6) / 2 = 1.85
Step 6: Calculate coefficient of quartile deviation:
Coefficient of quartile deviation = (Quartile deviation / (Q3 + Q1) / 2) x 100
Coefficient of quartile deviation = (1.85 / (42.3 + 38.6) / 2) x 100 = 5.68%
Therefore, the quartile deviation is 1.85 and the coefficient of quartile deviation is 5.68%.
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Continuous series Calculate quartile deviation and the coefficient of quartile deviation from the following data.Wages in rupees per day lesser than 35-37 38-40 41-43 over 43Number of wages 14 62 99 18 7 Related: Quartile Deviation - Measures of Dispersion, Business Mathematics & Statistics?
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Continuous series Calculate quartile deviation and the coefficient of quartile deviation from the following data.Wages in rupees per day lesser than 35-37 38-40 41-43 over 43Number of wages 14 62 99 18 7 Related: Quartile Deviation - Measures of Dispersion, Business Mathematics & Statistics? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about Continuous series Calculate quartile deviation and the coefficient of quartile deviation from the following data.Wages in rupees per day lesser than 35-37 38-40 41-43 over 43Number of wages 14 62 99 18 7 Related: Quartile Deviation - Measures of Dispersion, Business Mathematics & Statistics? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Continuous series Calculate quartile deviation and the coefficient of quartile deviation from the following data.Wages in rupees per day lesser than 35-37 38-40 41-43 over 43Number of wages 14 62 99 18 7 Related: Quartile Deviation - Measures of Dispersion, Business Mathematics & Statistics?.
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