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Mathematics and Statistics · Class 11 Commerce

Ch 11Measures of Dispersion — Class 11 Mathematics and Statistics, concept-first.

An average (mean, median or mode) tells us the central value of a set of data, but two very different sets can share the same average. Consider the daily earnings (in ₹) of two small shops over five days:

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Range and Coefficient of Range

Range and Coefficient of Range

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In previous exams

How often this chapter’s concepts have been examined — real appearance data, never estimated.

MHT-CET

1 concept · 3 appearances

2023, 2021

CA Foundation

1 concept · 2 appearances

2024

Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

1

Meaning of Dispersion; Absolute and Relative Measures

An average (mean, median or mode) tells us the central value of a set of data, but two very different sets can share the same average.

2

Range and Coefficient of Range

The Range is the simplest measure of dispersion — the difference between the largest and smallest values in the data.

3

Quartile Deviation (Semi-Interquartile Range)

The range depends only on the two extremes. The Quartile Deviation improves on this by using the quartiles, which describe the middle of the data and ignore the outer tails.

4

Mean Deviation

The range and quartile deviation both ignore most of the data. The Mean Deviation (M.D.) uses every value: it is the average of how far each value lies from a central value (the mean or the median), c…

5

Variance and Standard Deviation for Raw Data

The Standard Deviation is the most important and most widely used measure of dispersion. Instead of taking absolute values (as the mean deviation does), it squares each deviation from the mean — squar…

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Standard Deviation for a Frequency Distribution (Discrete and Continuous)

When data is given as a frequency distribution, each distinct value (or class mid-point) occurs times, so it must be weighted by its frequency.

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Coefficient of Variation

The standard deviation is an absolute measure, so it cannot fairly compare two data sets that have different averages or different units.

8

Combined Standard Deviation

Sometimes two groups are described separately (each by its size, mean and standard deviation) and we need the mean and standard deviation of the two groups taken together, without going back to the in…

Exercises

+Show 6 questions6 questions
  1. Q10Find the range and coefficient of range for the data: $25, 30, 18, 45, 52, 33$.Free
  2. Q11Find the quartile deviation and its coefficient for: $5, 8, 12, 15, 18, 21, 25, 28, 30, 34$.Free
  3. Q12Find the mean deviation from the mean, and its coefficient, for the frequency distribution: | $x$ | 10 | 20 | 30 | 40 | 50 | |---|---|---|--…Preview
  4. Q13Find the standard deviation of the following continuous frequency distribution by the step-deviation method: | Class | 0–20 | 20–40 | 40–60…Preview
  5. Q14Find the coefficient of variation for the data: $8, 10, 12, 14, 16$.Preview
  6. Q15Which one of the following is a RELATIVE measure of dispersion? (a) Range (b) Standard deviation (c) Coefficient of variation (d) Quartile d…Preview

More questions

+Show 9 questions9 questions
  1. Example 1Find the range and the coefficient of range for the following marks: $9, 11, 14, 15, 21, 22, 27, 29$.Free
  2. Example 2Find the quartile deviation and its coefficient for the data: $12, 15, 18, 20, 22, 25, 28, 30, 35$.Free
  3. Example 3Find the mean deviation from the mean, and its coefficient, for the data: $3, 6, 9, 12, 15$.Free
  4. Example 4Find the mean deviation from the median, and its coefficient, for the data: $4, 6, 8, 10, 12, 14, 16$.Preview
  5. Example 5Find the variance and standard deviation of: $2, 4, 6, 8, 10$.Preview
  6. Example 6Find the standard deviation of the following discrete frequency distribution: | $x$ | 10 | 20 | 30 | 40 | 50 | |---|---|---|---|---|---| | $…Preview
  7. Example 7Find the mean and standard deviation of the following continuous frequency distribution by the step-deviation method: | Class | 0–10 | 10–20…Preview
  8. Example 8Two batsmen A and B have the following batting records over a season: | | Mean score | Standard deviation | |---|---|---| | Batsman A | 50 |…Preview
  9. Example 9Two groups of items have the following statistics. Group 1: $40$ items, mean $30$, standard deviation $4$. Group 2: $60$ items, mean $35$, s…Preview