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Statistics · Class 11 Commerce

Ch 3Measures of Central Tendency — Class 11 Statistics, concept-first.

Raw data — a long list of marks, wages, ages or sales figures — is hard to grasp at a glance. A measure of central tendency condenses an entire distribution into ONE single, representative value around which most of the observations tend to cluster.

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Key concepts

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Median

Imagine you and four friends are comparing pocket money. The amounts are: ₹20, ₹50, ₹30, ₹100, ₹40. If you line these up from smallest to largest — ₹20, ₹30, ₹40, ₹50, ₹100 — the middle value is ₹40.

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In previous exams

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CA Foundation

2 concepts · 15 appearances

2026, 2025, 2023, 2022

Chapter contents

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

1

Meaning, Objectives and Types of Series

Raw data — a long list of marks, wages, ages or sales figures — is hard to grasp at a glance. A measure of central tendency condenses an entire distribution into ONE single, representative value aroun…

2

Arithmetic Mean — Computation, Merits and Limitations

Arithmetic mean (AM), commonly just called the "mean" or "average," is the sum of all observations divided by their number.

3

Median — Computation, Merits and Limitations

Median is the value of the middle-most observation when the data is arranged in ascending (or descending) order — it divides the distribution into two exactly equal halves, half the observations lying…

4

Mode — Computation, Merits and Limitations

Mode is the value that occurs most frequently in a data set — the observation with the highest concentration of items around it.

5

Geometric Mean — Computation, Merits and Limitations

Geometric mean (GM) is the root of the product of positive observations. It is the correct average to use whenever data involves rates of change, ratios, growth rates or index numbers — situations whe…

6

Harmonic Mean — Computation, Merits and Limitations

Harmonic mean (HM) is defined as the reciprocal of the arithmetic mean of the reciprocals of the observations.

7

Relationship Among AM, GM and HM; Choosing the Right Average

For ANY set of two or more positive observations that are not all equal, the three means always stand in the following fixed order:

Exercises

+Show 7 questions7 questions
  1. Q9Find the median of the following marks obtained by 5 students: 12, 15, 11, 18, 14.Free
  2. Q10Find the mode of the following discrete series: | x | 5 | 10 | 15 | 20 | |---|---|---|---|---| | f | 3 | 7 | 9 | 4 |Free
  3. Q11The average marks of 20 students in Section A is 50, and the average marks of 30 students in Section B is 60. Find the combined average mark…Free
  4. Q12A student scored 80 marks in a subject weighted 3, 70 marks in a subject weighted 2, and 90 marks in a subject weighted 1. Find the weighted…Preview
  5. Q13For any set of positive, unequal observations, which of the following relationships always holds? (a) AM > GM > HM (b) HM > GM > AM (c) AM =…Preview
  6. Q14For a certain distribution, the arithmetic mean is 45 and the median is 48. Estimate the mode using the empirical relationship, and verify y…Preview
  7. Q15Compare the median with the arithmetic mean: state two situations where median is preferable to mean, and one genuine limitation of median t…Preview

More questions

+Show 8 questions8 questions
  1. Example 1The marks obtained by 5 students in a Statistics test are 45, 60, 55, 70 and 50. Calculate the arithmetic mean by the direct method, and ver…Free
  2. Example 2Find the arithmetic mean of the following discrete series by the direct method, and verify using the step-deviation method: | x | 10 | 20 |…Free
  3. Example 3Calculate the arithmetic mean of the following continuous distribution using the step-deviation method, and verify using the direct method:…Free
  4. Example 4Using the same distribution as the previous example, calculate the median: | Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | |---|---|---|---…Preview
  5. Example 5Find the median of the following discrete series: | x | 10 | 20 | 30 | 40 | 50 | |---|---|---|---|---|---| | f | 4 | 6 | 10 | 8 | 2 |Preview
  6. Example 6Using the same distribution as Example 3, calculate the mode: | Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | |---|---|---|---|---|---| | N…Preview
  7. Example 7Find the geometric mean of the observations 2, 4 and 8, both directly and using logarithms.Preview
  8. Example 8A car travels equal distances at speeds of 40 km/hr, 60 km/hr and 80 km/hr on three successive stretches. Find the average speed for the who…Preview