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Measures of Central Tendency – Class 11 Economics notes, important questions and MCQs

NCERT Class 11 Economics, chapter 5. Notes, key terms, important questions with answers and MCQs.

Chapter overview

A measure of central tendency is a single value that represents the whole set of data. The three common averages are the arithmetic mean, the median and the mode. Each has its own merits and is suitable in different situations; for example, the median is better than the mean when there are extreme values.

Arithmetic mean

Arithmetic mean = sum of observations ÷ number of observations (Σx ÷ n).
For a frequency distribution, mean = Σfx ÷ Σf, where x is the value or class mark.
The mean uses all values but is affected by extreme values; the sum of deviations from the mean is zero.

Median and quartiles

The median is the middle value when data are arranged in order; its position is the (n + 1) ÷ 2 th item.
The median is not affected by extreme values, so it is useful for data such as income.
Quartiles divide the data into four equal parts; Q2 is the median.

Mode

The mode is the value that occurs most frequently.
It is useful for qualitative or popular choices, such as the most demanded shoe size.
In a moderately skewed distribution, mode ≈ 3 median − 2 mean.

Key terms

Central tendency: a single value that represents the centre of a data set
Arithmetic mean: the sum of all observations divided by their number
Median: the middle value of data arranged in ascending or descending order
Mode: the value that occurs most often in a data set
Quartile: a value that divides ordered data into four equal parts

Important questions with answers

Find the median of 10, 4, 8, 6, 12 and 2.2 marks

Arranged in order the data are 2, 4, 6, 8, 10, 12. With n = 6, the median is the average of the 3rd and 4th items, so median = (6 + 8) ÷ 2 = 7.

Why is the median preferred to the mean in some cases?3 marks

The median depends only on the middle position and is not affected by extreme values, while the mean is pulled up or down by very large or very small values. So for data such as income or wealth, where a few people have very high values, the median gives a better idea of the typical value. It can also be found for open-ended classes.

Compare the arithmetic mean, median and mode, giving their merits, demerits and uses.5 marks

The arithmetic mean is the sum of all observations divided by their number (Σx ÷ n, or Σfx ÷ Σf for a frequency distribution). It is easy to calculate, uses all observations, is rigidly defined and is useful for further algebraic work, such as finding total output from average output. However, it is affected by extreme values and may not be an actual value in the data. The median is the middle value of ordered data, located at the (n + 1) ÷ 2 th item. It is not affected by extreme values, can be found for open-ended classes and graphically from ogives, so it is suitable for income and wealth data; but it ignores the actual size of other values and is less useful for algebra. The mode is the most frequent value. It is simple, not affected by extreme values and useful for qualitative data and business decisions, such as the most popular size of shoes; but it may be ill-defined or there may be more than one mode. In a moderately skewed distribution the three are related as mode ≈ 3 median − 2 mean. The choice of average depends on the nature of the data and the purpose of the study.

Quick revision

Mean = Σx ÷ n; Σfx ÷ Σf.
Median = (n + 1) ÷ 2 th item.
Mode = most frequent value.
Mode ≈ 3 median − 2 mean.

Exam tips

Write the formula first, then substitute values, then give the answer with units.
Remember when to use each average: mean for balanced data, median with extreme values, mode for most common item.

Practice MCQs

The mean of 2, 4, 6, 8 and 10 is
1. 5
2. 30
3. 6
4. 8
Show answer
Answer: (c) 6. 30 ÷ 5 = 6.
The value that occurs most often is the
1. mean
2. median
3. range
4. mode
Show answer
Answer: (d) mode. It shows the most common item.
The middle value of ordered data is the
1. median
2. mean
3. mode
4. quartile Q3
Show answer
Answer: (a) median. It divides data into two equal halves.
The median of 3, 7, 9, 12 and 15 is
1. 7
2. 9
3. 12
4. 46
Show answer
Answer: (b) 9. It is the 3rd of 5 ordered values.
Which average is most affected by extreme values
1. arithmetic mean
2. mode
3. median
4. quartile
Show answer
Answer: (a) arithmetic mean. It uses every value.
If mean = 20 and median = 22, the mode by the empirical formula is about
1. 26
2. 24
3. 18
4. 21
Show answer
Answer: (a) 26. 3 × 22 − 2 × 20 = 26.
The sum of deviations of observations from their arithmetic mean is always
1. positive
2. negative
3. equal to n
4. zero
Show answer
Answer: (d) zero. This is a property of the mean.
Which average is most suitable for finding the typical income in a town with a few very rich people
1. arithmetic mean
2. sum
3. median
4. maximum
Show answer
Answer: (c) median. It is not distorted by extreme incomes.

All chapters of Class 11 Economics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.