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The following are the marks of 150 students in an examination.calculate karl pearson's coefficient of skewness Marks 0-10,10-20,20-30,30-40,40-50,50-60,60-70,70-80,80-90
no of students 20,10,40,0,15,20,15,10,30?
no of students 20,10,40,0,15,20,15,10,30?
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The following are the marks of 150 students in an examination.calculat...
Calculation of Karl Pearson's Coefficient of Skewness for Marks of 150 Students
Karl Pearson's Coefficient of Skewness is a measure of the degree of asymmetry of a distribution. It determines the direction and extent of deviation of a distribution from the normal distribution. The formula for calculating Karl Pearson's Coefficient of Skewness is:
Skewness = (3 * Mean - Mode) / Standard Deviation
where,
Mean = Sum of all observations / Total number of observations
Mode = Value that occurs most frequently in the distribution
Standard Deviation = Square root of [(Sum of (Observation - Mean)^2) / Total number of observations]
Step 1: Calculate the Mean, Mode, and Standard Deviation
To calculate the mean, mode, and standard deviation for the given data, we first need to find the midpoints of each class interval. The midpoints can be calculated as:
Midpoint = (Lower limit + Upper limit) / 2
Using this formula, we get the following midpoints:
5, 15, 25, 35, 45, 55, 65, 75, 85
Next, we calculate the mean using the formula:
Mean = Sum of all observations / Total number of observations
Mean = (20*5 + 10*15 + 40*25 + 0*35 + 15*45 + 20*55 + 15*65 + 10*75 + 30*85) / 150 = 43
The mode is the class interval with the highest frequency, which in this case is 20-30.
The standard deviation can be calculated using the formula:
Standard Deviation = Square root of [(Sum of (Observation - Mean)^2) / Total number of observations]
Standard Deviation = √[((20-43)^2*20 + (10-43)^2*10 + (40-43)^2*40 + (0-43)^2*0 + (15-43)^2*15 + (20-43)^2*20 + (15-43)^2*15 + (10-43)^2*10 + (30-43)^2*30) / 150] = 21.84
Step 2: Calculate the Skewness
Using the formula for Karl Pearson's Coefficient of Skewness, we can calculate the skewness as:
Skewness = (3 * Mean - Mode) / Standard Deviation
Skewness = (3 * 43 - 25) / 21.84 = 0.86
Interpretation of Result
The skewness value of 0.86 indicates that the distribution is moderately skewed to the right. This means that there are more students with lower marks and fewer students with higher marks. The distribution is not symmetric and has a longer tail towards the higher marks.
Karl Pearson's Coefficient of Skewness is a measure of the degree of asymmetry of a distribution. It determines the direction and extent of deviation of a distribution from the normal distribution. The formula for calculating Karl Pearson's Coefficient of Skewness is:
Skewness = (3 * Mean - Mode) / Standard Deviation
where,
Mean = Sum of all observations / Total number of observations
Mode = Value that occurs most frequently in the distribution
Standard Deviation = Square root of [(Sum of (Observation - Mean)^2) / Total number of observations]
Step 1: Calculate the Mean, Mode, and Standard Deviation
To calculate the mean, mode, and standard deviation for the given data, we first need to find the midpoints of each class interval. The midpoints can be calculated as:
Midpoint = (Lower limit + Upper limit) / 2
Using this formula, we get the following midpoints:
5, 15, 25, 35, 45, 55, 65, 75, 85
Next, we calculate the mean using the formula:
Mean = Sum of all observations / Total number of observations
Mean = (20*5 + 10*15 + 40*25 + 0*35 + 15*45 + 20*55 + 15*65 + 10*75 + 30*85) / 150 = 43
The mode is the class interval with the highest frequency, which in this case is 20-30.
The standard deviation can be calculated using the formula:
Standard Deviation = Square root of [(Sum of (Observation - Mean)^2) / Total number of observations]
Standard Deviation = √[((20-43)^2*20 + (10-43)^2*10 + (40-43)^2*40 + (0-43)^2*0 + (15-43)^2*15 + (20-43)^2*20 + (15-43)^2*15 + (10-43)^2*10 + (30-43)^2*30) / 150] = 21.84
Step 2: Calculate the Skewness
Using the formula for Karl Pearson's Coefficient of Skewness, we can calculate the skewness as:
Skewness = (3 * Mean - Mode) / Standard Deviation
Skewness = (3 * 43 - 25) / 21.84 = 0.86
Interpretation of Result
The skewness value of 0.86 indicates that the distribution is moderately skewed to the right. This means that there are more students with lower marks and fewer students with higher marks. The distribution is not symmetric and has a longer tail towards the higher marks.
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The following are the marks of 150 students in an examination.calculate karl pearson's coefficient of skewness Marks 0-10,10-20,20-30,30-40,40-50,50-60,60-70,70-80,80-90 no of students 20,10,40,0,15,20,15,10,30?
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The following are the marks of 150 students in an examination.calculate karl pearson's coefficient of skewness Marks 0-10,10-20,20-30,30-40,40-50,50-60,60-70,70-80,80-90 no of students 20,10,40,0,15,20,15,10,30? 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 The following are the marks of 150 students in an examination.calculate karl pearson's coefficient of skewness Marks 0-10,10-20,20-30,30-40,40-50,50-60,60-70,70-80,80-90 no of students 20,10,40,0,15,20,15,10,30? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following are the marks of 150 students in an examination.calculate karl pearson's coefficient of skewness Marks 0-10,10-20,20-30,30-40,40-50,50-60,60-70,70-80,80-90 no of students 20,10,40,0,15,20,15,10,30?.
The following are the marks of 150 students in an examination.calculate karl pearson's coefficient of skewness Marks 0-10,10-20,20-30,30-40,40-50,50-60,60-70,70-80,80-90 no of students 20,10,40,0,15,20,15,10,30? 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 The following are the marks of 150 students in an examination.calculate karl pearson's coefficient of skewness Marks 0-10,10-20,20-30,30-40,40-50,50-60,60-70,70-80,80-90 no of students 20,10,40,0,15,20,15,10,30? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following are the marks of 150 students in an examination.calculate karl pearson's coefficient of skewness Marks 0-10,10-20,20-30,30-40,40-50,50-60,60-70,70-80,80-90 no of students 20,10,40,0,15,20,15,10,30?.
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