CBSE Class 11 Economics Chapter 5: Measures of Central Tendency NCERT Solutions
This chapter, "Measures of Central Tendency," for CBSE Class 11 Economics, delves into the fundamental concepts of statistical averages. The NCERT Solutions provide clear explanations and applications of Mean, Median, and Mode, helping students understand which measure is most appropriate for different types of data and scenarios. The solutions cover practical examples, including choosing the right average for garment sizes, student intelligence, production figures, wages, and data with extreme values or open-ended distributions. By working through these exercises, students will develop a strong foundation in descriptive statistics, essential for data analysis and interpretation in economics. These solutions are designed to aid students in mastering these core concepts for their upcoming examinations, offering step-by-step guidance and reinforcing key statistical principles.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 11 |
| Subject | Economics |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | Chapter 5 |
Chapter summary
Chapter 5 of the CBSE Class 11 Economics syllabus focuses on Measures of Central Tendency. This section of NCERT Solutions explains the three main types of averages: Mean, Median, and Mode. It guides students on selecting the appropriate measure based on the nature of the data, whether it's qualitative or quantitative, and the presence of extreme values or open-ended distributions. The exercises reinforce the understanding of when to use each measure, particularly highlighting the properties and applications of Mode, Median, and Arithmetic Mean.
Learning outcomes
- Understand the concept of central tendency in statistics.
- Identify and differentiate between Mean, Median, and Mode.
- Determine the most suitable measure of central tendency for various data types and scenarios.
- Explain the properties and applications of Mode, Median, and Arithmetic Mean.
- Solve problems involving the selection of appropriate averages for given contexts.
Topics covered
Paper topics
- Measures of Central Tendency
- Arithmetic Mean
- Median
- Mode
- Qualitative Measurement
- Quantitative Measurement
- Extreme Items
- Open-ended Frequency Distribution
- Sum of Deviations
- Ratios
Important topics
- Choosing the appropriate measure of central tendency
- Properties of Mean, Median, and Mode
- Application of Mode for qualitative data
- Application of Median for open-ended distributions
- Impact of extreme values on Arithmetic Mean
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Questions and Solutions
Q1. Which average would be suitable in the following cases?
(i) Average size of readymade garments.
(ii) Average intelligence of students in a class.
(iii) Average production in a factory per shift.
(iv) Average wage in an industrial concern.
(v) When the sum of absolute deviations from average is least.
(vi) When quantities of the variable are in ratios.
(vii) In case of open-ended frequency distribution.
Solution:
(i) Mode would be the most suitable average for determining the average size of readymade garments. This is because the mode represents the most frequently occurring size, which is essential for inventory management and production planning.
(ii) Median is the most appropriate average for measuring the average intelligence of students in a class. Intelligence is a qualitative characteristic, and the median is better suited for such data as it represents the middle value when data is ordered, unaffected by extreme scores.
(iii) Arithmetic Mean is suitable for calculating the average production in a factory per shift. Production is a quantitative measure, and the arithmetic mean provides a precise average value by considering all production figures.
(iv) Arithmetic Mean is the appropriate average for the average wage in an industrial concern. Wages are quantitative data, and the arithmetic mean effectively represents the typical wage earned by employees in that concern.
(v) When the sum of absolute deviations from an average is least, the Arithmetic Mean is the suitable average. A key property of the arithmetic mean is that the sum of the absolute deviations of the data points from the mean is minimized compared to any other point.
(vi) When quantities of the variable are expressed in ratios, the Arithmetic Mean is generally suitable. Ratios represent quantitative relationships, and the arithmetic mean can be used to find the average ratio.
(vii) In the case of an open-ended frequency distribution, the Median is the most appropriate measure of central tendency. This is because the median can be calculated without needing the exact limits of the open-ended classes, unlike the arithmetic mean.
Q2. Indicate the most appropriate alternative from the multiple choices provided against each question.
(i) The most suitable average for qualitative measurement is
(a) Arithmetic mean
(b) Median
(c) Mode
(d) Geometric mean
(e) None of the above
Solution: The most appropriate alternative is (c) Mode. The mode is the value that appears most frequently in a data set and is best suited for qualitative data where categories or characteristics are being described, rather than numerical values.
(ii) Which average is affected most by the presence of extreme items?
(a) Median
(b) Mode
(c) Arithmetic mean
(d) None of the above
Solution: The average most affected by the presence of extreme items is (c) Arithmetic mean. Extreme values (very large or very small numbers) can significantly pull the arithmetic mean towards them, thus distorting its representation of the central tendency of the data.
(iii) The algebraic sum of deviation of a set of n values from A.M is
(a) N
(b) 0
(c) 1
(d) none of the above
Solution: The algebraic sum of deviations of a set of 'n' values from their Arithmetic Mean (A.M.) is (b) 0. This is a fundamental property of the arithmetic mean: the sum of the differences between each data point and the mean is always zero.
Common mistakes
- Confusing the conditions for using Mode versus Median for qualitative data or open-ended distributions.
- Incorrectly identifying the measure most affected by extreme values.
- Misunderstanding the algebraic sum of deviations from the Arithmetic Mean.
Revision tips
- Focus on the specific scenarios provided in Q1 to understand when each measure (Mean, Median, Mode) is most appropriate.
- Memorize the key properties of each average, especially how they handle qualitative data and extreme values.
- Pay close attention to the explanation for the algebraic sum of deviations from the Mean in Q2(iii).
- Practice identifying the best average for different types of data presented in real-world economic contexts.
Practice MCQs
Q1. For qualitative measurement, which average is generally considered most suitable?
Explanation: Mode is the most appropriate average for qualitative measurements as it represents the most frequently occurring value or category.
Q2. Which measure of central tendency is most significantly influenced by extreme values in a dataset?
Explanation: The Arithmetic Mean is highly sensitive to extreme values (outliers) because it includes every value in its calculation.
Q3. What is the algebraic sum of deviations of a set of 'n' values from their Arithmetic Mean?
Explanation: A fundamental property of the Arithmetic Mean is that the sum of the deviations of all observations from the mean is always zero.
Q4. In the context of readymade garments, which average is typically used to determine the 'average size'?
Explanation: Mode is suitable for garment sizes as it indicates the most commonly purchased or produced size, which is crucial for inventory and production.
Q5. For an open-ended frequency distribution, which measure of central tendency is often preferred?
Explanation: Median is preferred for open-ended distributions because its calculation does not require specific class limits for the open-ended classes.
Frequently asked questions
What are the main measures of central tendency discussed in this chapter?
This chapter focuses on the three primary measures of central tendency: the Arithmetic Mean, the Median, and the Mode.
When is the Mode the most suitable average to use?
The Mode is most suitable for qualitative measurements, such as the average size of readymade garments or average intelligence, as it represents the most frequent value.
Why is the Median often preferred for open-ended frequency distributions?
The Median is preferred because its calculation does not require specific class limits for the open-ended classes, unlike the Mean.
How do extreme values affect the Arithmetic Mean?
Extreme values, or outliers, significantly influence the Arithmetic Mean because it takes into account every value in the dataset for its calculation.
What is a key property of the Arithmetic Mean regarding deviations?
A key property is that the algebraic sum of deviations of all observations from the Arithmetic Mean is always zero.
How can these NCERT Solutions help with exam preparation?
These solutions provide clear explanations and detailed answers to common questions about central tendency, helping students understand the concepts and apply them correctly for exam revision.
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