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Calculate standard deviation and coefficient of variation from the following data Marks. Number of students Below 20 8 Below 40. 20 Below 60. 50 Below 80. 70 Below 100. 80?
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Calculating Standard Deviation and Coefficient of Variation
- Step 1: Find the class marks
- Step 2: Find the mean
- Step 3: Find the deviations
- Step 4: Find the squared deviations
- Step 5: Find the variance
- Step 6: Find the standard deviation
- Step 7: Find the coefficient of variation
Class marks refer to the mid-point of the range of each class. For example, for the first class, the range is 0-20. The mid-point of this range is 10. So, we can say that the class mark for the first class is 10.
The mean is the average of the class marks. To find the mean, we add up all the class marks and divide by the total number of students:
(8*10 + 20*30 + 50*50 + 70*90 + 80*90) / 298 = 64.43
The deviation is the difference between each class mark and the mean. To find the deviation, we subtract the mean from each class mark:
8: (10 - 64.43) = -54.43
20: (30.43) = -34.43
50: (85.57) = -14.43
70: (25.57) = 5.57
80: (25.57) = 15.57
We square each deviation to remove negative signs:
8: (-54.43)^2 = 2961.70
20: (-34.43)^2 = 1183.22
50: (-14.43)^2 = 208.36
70: (5.57)^2 = 31.02
80: (15.57)^2 = 242.29
The variance is the sum of the squared deviations divided by the total number of students minus one:
(2961.70 + 1183.22 + 208.36 + 31.02 + 242.29) / (298 - 1) = 1969.69
The standard deviation is the square root of the variance:
sqrt(1969.69) = 44.38
The coefficient of variation is the ratio of the standard deviation to the mean, expressed as a percentage:
(44.38 / 64.43) x 100% = 68.83%
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Calculate standard deviation and coefficient of variation from the following data Marks. Number of students Below 20 8 Below 40. 20 Below 60. 50 Below 80. 70 Below 100. 80?
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Calculate standard deviation and coefficient of variation from the following data Marks. Number of students Below 20 8 Below 40. 20 Below 60. 50 Below 80. 70 Below 100. 80? for Commerce 2024 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about Calculate standard deviation and coefficient of variation from the following data Marks. Number of students Below 20 8 Below 40. 20 Below 60. 50 Below 80. 70 Below 100. 80? covers all topics & solutions for Commerce 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate standard deviation and coefficient of variation from the following data Marks. Number of students Below 20 8 Below 40. 20 Below 60. 50 Below 80. 70 Below 100. 80?.
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