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NCERT Solutions for Class 11 Math Ch-13: Statistics
NCERT Solutions for Class 11 Maths Chapter 13 Statistics covers measures of dispersion including range, mean deviation, variance, and standard deviation for both grouped and ungrouped data.
Overview of Topics & Subtopics
Important Questions and Answers
Q1: What is meant by 'range' as a measure of dispersion, and how is it calculated?
Answer: Range is the simplest measure of dispersion of a data set, calculated as the difference between the maximum and minimum values in the data set: Range = Maximum value − Minimum value.
Q2: What is mean deviation, and how is mean deviation about the mean calculated for ungrouped data?
Answer: Mean deviation measures the average of the absolute deviations of data points from a central value (mean or median). For ungrouped data, mean deviation about the mean is calculated as MD = (1/n) Σ|xi − x̄|, where x̄ is the mean of the observations.
Q3: Define variance and standard deviation.
Answer: Variance is defined as the mean of the squared deviations of observations from their mean, given by σ² = (1/n) Σ(xi − x̄)². Standard deviation is the positive square root of the variance, σ = √variance, and it is expressed in the same units as the original data.
Q4: Why is standard deviation generally preferred over mean deviation as a measure of dispersion?
Answer: Standard deviation is generally preferred because it uses the actual squared deviations (avoiding the need for absolute values), making it more mathematically manageable for further statistical analysis, and it also gives greater weight to larger deviations from the mean.
Q5: What does a lower standard deviation indicate about a data set compared to a higher one?
Answer: A lower standard deviation indicates that the data points are more closely clustered around the mean (less variability), while a higher standard deviation indicates that the data points are more widely spread out from the mean (greater variability).
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