Statistics · Class 11 Commerce
Ch 4Measures of Dispersion — Class 11 Statistics, concept-first.
Central tendency measures such as the mean, median, and mode locate the centre of a data set, but two data sets can have exactly the same average value and still be very different in how their individual observations are spread out around that average.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Standard Deviation, Variance and Coefficient of Variation
Standard Deviation () is the square root of Variance (), the mean of the squared deviations of all observations from the arithmetic mean: , computable either by the direct (actual mean) method or the equivalent short-cut…
Most relevant Q&A
- The runs scored by two batsmen, A and B, over a season give: Batsman A — Mean = 50 runs, Standard Deviation = 5 runs. Batsman B — Mean = 60…Free
- Find the Variance and Standard Deviation of the data: 3, 6, 9, 12, 15.Preview
- Compute the Variance and Standard Deviation of the following distribution using the step-deviation method: | Marks | 0–10 | 10–20 | 20–30 |…Preview
- Which of the following measures of dispersion is considered the most reliable, since it is based on every observation and permits further al…Free
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Meaning and Need for Measures of Dispersion
Central tendency measures such as the mean, median, and mode locate the centre of a data set, but two data sets can have exactly the same average value and still be very different in how their individ…
Absolute and Relative Measures of Dispersion
Measures of dispersion are classified into two broad types:
Range and Coefficient of Range
Range is the simplest measure of dispersion — the difference between the largest () and smallest () values in a data set.
Quartile Deviation and Coefficient of Quartile Deviation
Quartile Deviation (Q.D.), also called the semi-inter-quartile range, is based on the middle 50% of the data — it ignores the extreme 25% of values on each end, which makes it more stable than the Ran…
Mean Deviation and Coefficient of Mean Deviation
Mean Deviation (M.D.) measures the average of the absolute deviations of every observation from a chosen central value — usually the mean or the median (deviations are taken as absolute values, ignori…
Standard Deviation and Variance
Standard Deviation (S.D., denoted ) is the most widely used and most reliable measure of dispersion. It is the positive square root of the variance (), the mean of the squared deviations of all observ…
Coefficient of Variation
Standard Deviation is an absolute measure — it carries the same unit as the original data — so it cannot, by itself, be used to compare the variability of two series that are in different units or hav…
Exercises
More questions
10 Q+−Show 8 questionsHide questions8 questions
- Example 1The marks (out of 100) obtained by 10 students in a Statistics test are: 45, 52, 38, 60, 41, 55, 48, 63, 50, 42. Find the Range and the Coef…Free
- Example 2Find the Range and Coefficient of Range for the following distribution of the daily wages of workers in a factory: | Wages (Rs.) | 10–20 | 2…Free
- Example 3Find the Quartile Deviation and its Coefficient for the following data (marks of 8 students, already arranged in ascending order): 10, 12, 1…Free
- Example 4Compute the Quartile Deviation and the Coefficient of Quartile Deviation for the following distribution of marks of 50 students: | Marks | 0…Preview
- Example 5Find the Mean Deviation about the Mean and its Coefficient for the data: 5, 8, 12, 15, 20.Preview
- Example 6The following table shows the number of children per family in a locality: | No. of children ($x$) | 2 | 4 | 6 | 8 | 10 | |---|---|---|---|-…Preview
- Example 7Find the Variance and Standard Deviation of the data: 3, 6, 9, 12, 15.Preview
- Example 8Compute the Variance and Standard Deviation of the following distribution using the step-deviation method: | Marks | 0–10 | 10–20 | 20–30 |…Preview