Important Questions and Answers for Class 11 Economics Chapter 5 Measures of Central Tendency 2025-26

1. The measure of central tendency which is affected by extreme values is:

• (a) Median
• (b) Mode
• (c) Arithmetic Mean
• (d) Range

Answer: (c) Arithmetic Mean. Arithmetic mean is influenced by extreme values in data as it considers all values in its calculation.

2. If a data set is: 8, 12, 12, 15, 16, then the mode is:

• (a) 8
• (b) 12
• (c) 15
• (d) 16

Answer: (b) 12. Mode is the value that occurs most frequently; here, 12 appears twice.

3. Which of the following is a positional average?

• (a) Arithmetic Mean
• (b) Weighted Mean
• (c) Median
• (d) Geometric Mean

Answer: (c) Median. Median is determined by the position of values in the arranged data set.

2. Very Short Answer (VSA).

1. Define 'central tendency' in statistics.

Answer: Central tendency is a statistical measure that identifies a single value as representative of an entire dataset, typically using the mean, median, or mode.

2. Write the formula for the arithmetic mean for ungrouped data.

Answer: The formula is $\bar{X} = \dfrac{X_1 + X_2 + ... + X_n}{n}$, where $X_i$ are observations and $n$ is their count.

3. What is the median of 5, 7, 6, 1, 8, 10, 12, 4, 3?

Answer: Arranged in ascending order, the median (middle value) is 6.

3. Short Answer Questions.

1. Distinguish between the arithmetic mean and mode with examples.

Answer: Arithmetic mean is the sum of all data points divided by the number of observations, while mode is the value that appears most frequently. For example, in 2, 3, 3, 4, the mean is 3, but the mode is also 3 as it occurs twice.

2. Why is the median preferred over the arithmetic mean in case of open-ended distributions?

Answer: Median is preferred because it is not affected by extreme or undefined values at the ends, providing a better central value, especially when class intervals are open-ended or data is skewed.

4. Long Answer Questions.

1. Explain with reasons the situations where mode is a more appropriate measure of central tendency than mean or median.

Answer: Mode is most appropriate when qualitative data or categorical variables are analyzed, as it shows the most frequently occurring value. It is particularly useful for items like "most popular shirt size" or "preferred product" where numerical averages are meaningless. In highly skewed data, mode indicates the most common observation.

1. Identify the context: categorical/qualitative or highly skewed data.
2. Calculate frequency of each category/value.
3. Mode is the value with the highest frequency.

2. Describe the step deviation method for calculating arithmetic mean with its advantages.

Answer: The step deviation method simplifies the calculation of the arithmetic mean when data values or deviations are large and follow regular intervals. By dividing deviations by a common factor, it makes computations easier and reduces clerical work, especially in grouped or continuous series.

1. Choose an assumed mean (A).
2. Compute deviations: $d = X - A$ for each value.
3. Divide each deviation by common factor $c$ to get $d' = (X - A)/c$.
4. Sum $d'$s and apply: $\bar{X} = A + \dfrac{\sum d'}{N} \times c$.

5. Assertion–Reason type questions.

Assertion (A): The sum of deviations from the arithmetic mean is always zero.
Reason (R): Arithmetic mean considers the magnitude and sign of all observations.

• (a) A and R are true, and R is the correct explanation of A
• (b) A and R are true, but R is not the correct explanation of A
• (c) A is true, but R is false
• (d) A is false, but R is true

Answer: (a) Both statements are true and R correctly explains A since arithmetic mean balances total positive and negative deviations.

Assertion (A): Mode is affected by extreme values.
Reason (R): Mode only considers the value with maximum frequency.

• (a) A and R are true, and R is the correct explanation of A
• (b) A and R are true, but R is not the correct explanation of A
• (c) A is true, but R is false
• (d) A is false, but R is true

Answer: (d) Assertion is false, but Reason is true. Mode does not get affected by extreme values as it is based only on frequency.

6. Case-based questions.

A small firm has ten employees. Their weekly wages (in Rs) are as follows: 800, 900, 850, 1200, 1500, 800, 950, 900, 920, 850. The manager wants to analyze the central tendency to make salary decisions.

(i) Which measure of central tendency would be most affected if two employees receive an extraordinary bonus?

Answer: Arithmetic mean, as it is influenced by extreme high/low values.

(ii) Find the mode of the data.

Answer: 800 and 900 (both occur twice; data is bimodal).

(iii) Why might the median offer a more accurate representation than the mean in this context?

Answer: Median is not affected by outliers or extreme wages, thus represents typical earnings better.

7. Match the following.

8. Numericals / Derivations.

1. Calculate the arithmetic mean for the following data set: 18, 24, 30, 28, 20.

Answer: The mean value is 24.

1. Given values: 18, 24, 30, 28, 20.
2. Formula: $\bar{X} = \dfrac{\sum X}{n}$
3. Sum: $18+24+30+28+20=120$
4. $n=5$, so $\bar{X} = 120/5 = 24$

2. Find the median of the following series: 25, 28, 27, 26, 30, 29.

Answer: Median is 27.5.

1. Arrange data: 25, 26, 27, 28, 29, 30
2. Number of values $n=6$ (even)
3. Median$= \frac{27+28}{2}=27.5$
4. So, median is 27.5

Benefits of Understanding About Measures of Central Tendency

Learn Statistics for Economics Class 11 Chapter 5 questions and answers to build strong fundamentals. Understanding mean, median and mode boosts concept clarity and exam confidence. Mastering these concepts is vital for scoring well and making data-based decisions in Economics.

Download our Economics Class 11 Important Questions with Answers PDF NCERT and major Measures of central tendency Class 11 numericals for ready practice. These expert-created resources help you solve real-life data sets, mastering both concepts and application for board success.