Statistics · Class 11 Commerce
Ch 5Skewness of Frequency Distribution — Class 11 Statistics, concept-first.
In your earlier chapters on Statistics you learned to summarise a frequency distribution using measures of central tendency (mean, median, mode) and measures of dispersion (range, quartile deviation, mean deviation, standard deviation).
Key concepts
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Bowley's Coefficient of Skewness
Bowley's coefficient of skewness, Sk = (Q3 + Q1 minus 2 times Median) divided by (Q3 minus Q1), is built entirely from the three quartiles, so it needs no standard deviation and remains computable even when a distributio…
Most relevant Q&A
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Meaning of Skewness: Symmetric and Skewed Distributions
In your earlier chapters on Statistics you learned to summarise a frequency distribution using measures of central tendency (mean, median, mode) and measures of dispersion (range, quartile deviation,…
Types of Skewness: Positive and Negative
A skewed distribution is classified by which tail is longer.
Absolute and Relative Measures of Skewness
Skewness can be measured in two ways.
Karl Pearson's Coefficient of Skewness
Karl Pearson's coefficient of skewness compares the mean and the mode (or, when the mode is unreliable, the mean and the median) relative to the standard deviation.
Bowley's Coefficient of Skewness
Karl Pearson's coefficient needs the mean, the mode (or median) and the standard deviation — all three calculations, including the standard deviation, which is the most laborious of the lot.
Comparing Karl Pearson's and Bowley's Measures
Both coefficients answer the same question — is the distribution symmetric, and if not, in which direction and to what degree — but they use different information and are not expected to give numerica…
Exercises
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- Q6The marks of 11 students, arranged in ascending order, are: 12, 15, 18, 20, 22, 25, 28, 30, 33, 38, 45. Compute Bowley's coefficient of skew…Free
- Q7Distinguish between Karl Pearson's coefficient of skewness and Bowley's coefficient of skewness. Under what circumstances would you prefer B…Free
- Q8In a perfectly symmetric distribution, Karl Pearson's coefficient of skewness is: (a) Positive (b) Negative (c) Zero (d) Equal to 3Preview
- Q9For a distribution of monthly savings of employees, the mean is Rs. 38 and the median is Rs. 36. The standard deviation is Rs. 8, and the mo…Preview
- Q10For a distribution, Mean = Median = Mode = 50. What can you conclude about the skewness of this distribution, without doing any further calc…Preview
More questions
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- Example 1What is a symmetric distribution? Distinguish it from a skewed distribution, and state the relationship among mean, median and mode in each…Free
- Example 2Explain positive and negative skewness with reference to the relative positions of mean, median and mode. What is the empirical relationship…Free
- Example 3The daily wages (in Rs.'00) of 9 workers in a small firm are: 20, 22, 25, 25, 25, 28, 30, 35, 40. Calculate Karl Pearson's coefficient of sk…Preview
- Example 4The following table gives the marks obtained by 50 students in a Statistics test. Calculate Karl Pearson's coefficient of skewness for this…Preview
- Example 5For the same marks distribution as Worked Example 4 (50 students; Marks 0-10:5, 10-20:8, 20-30:15, 30-40:12, 40-50:7, 50-60:3), calculate Bo…Preview