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The following table indicates the marks obtained by students in a statistics test: Marks Number of students 0-20 5 20-40 7 40-60 - 60-80 8 80-100 7 The arithmetic mean for the class was 52.5 marks. Required: a) Find the missing value (5 Marks) b) Find the standard deviation (11 Marks) c) Semi-interquartile range (6 Marks) d) Determine the coefficient of variance (3 Marks) e) Find the coefficient of skewness (5 Marks) ?
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The following table indicates the marks obtained by students in a stat...
Missing Value:
The total number of students is 27 (5+7+8+7). Since the arithmetic mean is 52.5, the total sum of marks is 52.5 x 27 = 1417.5. The sum of the known marks is 20 x 5 + 30 x 7 + 40 x 8 + 60 x 7 = 1340. Therefore, the missing value is 1417.5 - 1340 = 77.5.
Standard Deviation:
To find the standard deviation, we first need to calculate the variance. Using the formula for variance: variance = Σ(x - μ)² / n, where x is the value, μ is the mean, and n is the total number of values. After finding the variance, take the square root of it to get the standard deviation.
Semi-Interquartile Range:
To find the semi-interquartile range, first, calculate the first and third quartiles. Then subtract the first quartile from the third quartile, and divide the result by 2 to get the semi-interquartile range.
Coefficient of Variance:
To determine the coefficient of variance, divide the standard deviation by the mean and multiply by 100 to get the percentage.
Coefficient of Skewness:
The coefficient of skewness measures the symmetry of the data distribution. If the coefficient is 0, the distribution is perfectly symmetric. If it is positive, the distribution is skewed to the right, while a negative value indicates left skew. Calculate the coefficient of skewness using the formula: (mean - mode) / standard deviation.
The total number of students is 27 (5+7+8+7). Since the arithmetic mean is 52.5, the total sum of marks is 52.5 x 27 = 1417.5. The sum of the known marks is 20 x 5 + 30 x 7 + 40 x 8 + 60 x 7 = 1340. Therefore, the missing value is 1417.5 - 1340 = 77.5.
Standard Deviation:
To find the standard deviation, we first need to calculate the variance. Using the formula for variance: variance = Σ(x - μ)² / n, where x is the value, μ is the mean, and n is the total number of values. After finding the variance, take the square root of it to get the standard deviation.
Semi-Interquartile Range:
To find the semi-interquartile range, first, calculate the first and third quartiles. Then subtract the first quartile from the third quartile, and divide the result by 2 to get the semi-interquartile range.
Coefficient of Variance:
To determine the coefficient of variance, divide the standard deviation by the mean and multiply by 100 to get the percentage.
Coefficient of Skewness:
The coefficient of skewness measures the symmetry of the data distribution. If the coefficient is 0, the distribution is perfectly symmetric. If it is positive, the distribution is skewed to the right, while a negative value indicates left skew. Calculate the coefficient of skewness using the formula: (mean - mode) / standard deviation.
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The following table indicates the marks obtained by students in a statistics test: Marks Number of students 0-20 5 20-40 7 40-60 - 60-80 8 80-100 7 The arithmetic mean for the class was 52.5 marks. Required: a) Find the missing value (5 Marks) b) Find the standard deviation (11 Marks) c) Semi-interquartile range (6 Marks) d) Determine the coefficient of variance (3 Marks) e) Find the coefficient of skewness (5 Marks) ?
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The following table indicates the marks obtained by students in a statistics test: Marks Number of students 0-20 5 20-40 7 40-60 - 60-80 8 80-100 7 The arithmetic mean for the class was 52.5 marks. Required: a) Find the missing value (5 Marks) b) Find the standard deviation (11 Marks) c) Semi-interquartile range (6 Marks) d) Determine the coefficient of variance (3 Marks) e) Find the coefficient of skewness (5 Marks) ? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The following table indicates the marks obtained by students in a statistics test: Marks Number of students 0-20 5 20-40 7 40-60 - 60-80 8 80-100 7 The arithmetic mean for the class was 52.5 marks. Required: a) Find the missing value (5 Marks) b) Find the standard deviation (11 Marks) c) Semi-interquartile range (6 Marks) d) Determine the coefficient of variance (3 Marks) e) Find the coefficient of skewness (5 Marks) ? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following table indicates the marks obtained by students in a statistics test: Marks Number of students 0-20 5 20-40 7 40-60 - 60-80 8 80-100 7 The arithmetic mean for the class was 52.5 marks. Required: a) Find the missing value (5 Marks) b) Find the standard deviation (11 Marks) c) Semi-interquartile range (6 Marks) d) Determine the coefficient of variance (3 Marks) e) Find the coefficient of skewness (5 Marks) ?.
The following table indicates the marks obtained by students in a statistics test: Marks Number of students 0-20 5 20-40 7 40-60 - 60-80 8 80-100 7 The arithmetic mean for the class was 52.5 marks. Required: a) Find the missing value (5 Marks) b) Find the standard deviation (11 Marks) c) Semi-interquartile range (6 Marks) d) Determine the coefficient of variance (3 Marks) e) Find the coefficient of skewness (5 Marks) ? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The following table indicates the marks obtained by students in a statistics test: Marks Number of students 0-20 5 20-40 7 40-60 - 60-80 8 80-100 7 The arithmetic mean for the class was 52.5 marks. Required: a) Find the missing value (5 Marks) b) Find the standard deviation (11 Marks) c) Semi-interquartile range (6 Marks) d) Determine the coefficient of variance (3 Marks) e) Find the coefficient of skewness (5 Marks) ? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following table indicates the marks obtained by students in a statistics test: Marks Number of students 0-20 5 20-40 7 40-60 - 60-80 8 80-100 7 The arithmetic mean for the class was 52.5 marks. Required: a) Find the missing value (5 Marks) b) Find the standard deviation (11 Marks) c) Semi-interquartile range (6 Marks) d) Determine the coefficient of variance (3 Marks) e) Find the coefficient of skewness (5 Marks) ?.
Solutions for The following table indicates the marks obtained by students in a statistics test: Marks Number of students 0-20 5 20-40 7 40-60 - 60-80 8 80-100 7 The arithmetic mean for the class was 52.5 marks. Required: a) Find the missing value (5 Marks) b) Find the standard deviation (11 Marks) c) Semi-interquartile range (6 Marks) d) Determine the coefficient of variance (3 Marks) e) Find the coefficient of skewness (5 Marks) ? in English & in Hindi are available as part of our courses for Quant.
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