Q.Calculate the Arithmetic Mean from the data showing marks of students in a class in an economics test: 40, 50, 55, 78, 58.
Concept understanding — Arithmetic Mean Calculation
Arithmetic Mean in Economics — A First Look
You already use the arithmetic mean every day without thinking about it. If your friend says "my average speed was 40 km/h" or "the average price of a burger in this city is ₹80," they are talking about the arithmetic mean. It is the most natural way to find a "typical" value when you have a list of numbers.
The Intuition
Imagine you have five friends, and their monthly pocket money (in ₹) is: 500, 600, 700, 800, 900. If you wanted one number that "represents" all of them, you would add them all up and divide by the number of friends. That gives you ₹700. That ₹700 is the arithmetic mean — it is the value each person would get if all the pocket money were pooled and shared equally.
In economics, this idea is everywhere. When we talk about "average income" of a country, "average price" of a basket of goods, or "average product" of a worker, we are using the arithmetic mean to summarise a large set of data into a single, understandable number.
The Precise Meaning
The arithmetic mean is defined as the sum of all observations divided by the number of observations. For a set of n values x1,x2,x3,…,xn, the arithmetic mean xˉ (read as "x-bar") is:
xˉ=nx1+x2+x3+⋯+xn
Or, more compactly:
xˉ=n∑i=1nxi
Where:
- ∑ (sigma) means "sum of"
- xi represents each individual observation
- n is the total number of observations
xˉ=n∑xi
Why It Matters in Economics
Economics deals with aggregates — total production, total income, total expenditure. But a single total tells you nothing about the typical experience. If a country's total income is ₹100 lakh crore, is that because everyone is rich or because a few people are extremely rich? The arithmetic mean of income gives you a first approximation, though as you will learn later, it has limitations (the median is often better for income data because the mean is pulled by extreme values).
Here are the key places you will meet the arithmetic mean in your Class 11/12 syllabus:
1. Average Product (AP) in Production
When a firm hires workers, the total output changes. The average product of labour is the output per worker:
APL=LTP
Where TP is total product (total output) and L is the number of workers. This is simply the arithmetic mean of output per worker.
2. Average Revenue (AR) or Price
A firm sells different quantities at possibly different prices. The average revenue is total revenue divided by quantity sold:
AR=QTR
Since TR=P×Q for a single price, AR=P. But if prices vary, AR is the arithmetic mean price.
3. Average Cost (AC)
Total cost divided by output:
AC=QTC
This tells you the cost per unit — again, an arithmetic mean.
4. Simple Index Numbers (Price Index)
When constructing a simple (unweighted) price index, you take the arithmetic mean of price relatives:
P01=n∑P0P1×100
Where P1 is the current year price, P0 is the base year price, and n is the number of commodities. This is a direct application of the arithmetic mean formula.
The arithmetic mean is sensitive to extreme values. One very high or very low observation can pull the mean significantly. In income data, a few billionaires can make the "average income" look much higher than what a typical person earns. That is why economists often use the median for income — it is the middle value and is not affected by extremes.
How to Calculate It — Step by Step
Suppose you have the daily wages (in ₹) of 6 workers: 200, 250, 300, 350, 400, 500.
Step 1: Add all the wages: 200+250+300+350+400+500=2000
Step 2: Count the number of workers: n=6
Step 3: Divide: xˉ=62000=333.33
So the average daily wage is ₹333.33.
For Grouped Data (Frequency Distribution)
When data is given in a frequency table (e.g., income ranges with number of people), you cannot add individual values because you do not have them. Instead, you use the midpoint of each class interval as a representative value.
xˉ=∑fi∑fixi
Where:
- fi is the frequency of the i-th class
- xi is the midpoint of the i-th class
- ∑fi=N, the total number of observations
For grouped data, always find the class midpoint first: xi=2lower limit+upper limit. Then multiply each midpoint by its frequency, sum those products, and divide by total frequency.
A Final Thought
The arithmetic mean is your first tool for making sense of economic data. It is simple, intuitive, and widely used. But remember: it is only one measure. In economics, you will soon meet the median and mode, and you will learn when each is appropriate. For now, master the arithmetic mean — it is the foundation on which much of economic analysis is built.
For an individual (ungrouped) series like this one, the arithmetic mean is simply the sum of all the observations divided by how many there are.
Arithmetic Mean Xˉ=540+50+55+78+58=5281=56.2 marks.
The arithmetic mean of an individual (ungrouped) series is the sum of all observations divided by their number. Here the five marks add up to 281, so the average mark is 281÷5=56.2.
Concept
The arithmetic mean is the most common measure of central tendency. For an ungrouped (individual) series it is:
Xˉ=N∑X
where ∑X is the sum of the observations and N is the number of observations.
Working
The marks are: 40, 50, 55, 78, 58, so N=5.
∑X=40+50+55+78+58=281
Xˉ=5281=56.2
The arithmetic mean of the marks is 56.2.
Showing the 12 most recent of 13 on this concept.
- AHSEC Assam Higher Secondary 1st Year Class 11 (Commerce) 2025Set ANNUAL1 markMCQQ.Which of the following is a measure of central tendency?(a) Arithmetic mean(b) Median(c) Mode(d) All of these
›Reveal solutionSolution
Correct option: All of these.
Which of the following is a measure of central tendency? arithmetic mean, median and mode are all measures of central tendency.
✓Final answerAll of these.
- AHSEC Assam Higher Secondary 1st Year Class 11 (Commerce) 2025Set ANNUAL1 markMCQQ.Which of the following measures of central tendency is known as positional average?(a) Mean(b) Median(c) Mode(d) None of these
›Reveal solutionSolution
Correct option: Median.
Which measure of central tendency is known as a positional average? the median is a positional average (located by position, not calculated from all values).
✓Final answerMedian.
- AHSEC Assam Higher Secondary 1st Year Class 11 (Commerce) 2025Set ANNUAL1 markMCQQ.Which of the following statistical measures calculable in case of open-ended class?(a) Range(b) Median(c) Mean deviation(d) Standard deviation
›Reveal solutionSolution
Correct option: Median.
Which statistical measure is calculable in case of an open-ended class? the median (a positional measure) can be calculated for an open-ended class, unlike the mean/range/SD.
✓Final answerMedian.
- AHSEC Assam Higher Secondary 1st Year Class 11 (Commerce) 2025Set ANNUAL1 markMCQQ.The other name of semi-interquartile range is(a) mean deviation(b) quartile deviation(c) standard deviation(d) None of these
›Reveal solutionSolution
Correct option: quartile deviation.
The other name of semi-interquartile range is ___. the semi-interquartile range is another name for the quartile deviation (Q3 − Q1)/2.
✓Final answerquartile deviation.
- AHSEC Assam Higher Secondary 1st Year Class 11 (Commerce) 2025Set ANNUAL1 markMCQQ.Mean deviation is determined using which of the following formulas?(a) sigma / X-bar(b) (Q3 - Q1) / 2(c) square root of (Sum of fd-squared / N)(d) Sum of f|D| / N
›Reveal solutionSolution
Correct option: Sum of f|D| / N.
Mean deviation is determined using which formula? mean deviation = Σf|D| / N (the mean of the absolute deviations).
✓Final answerSum of f|D| / N.
- AHSEC Assam Higher Secondary 1st Year Class 11 (Commerce) 2025Set ANNUAL1 markMCQQ.Which of the following is not a pure (unitless) number?(a) Arithmetic mean(b) Correlation coefficient(c) Coefficient of variation(d) Index number
›Reveal solutionSolution
Correct option: Arithmetic mean.
Which of the following is not a pure (unitless) number? the arithmetic mean has the units of the data, so it is NOT a pure (unitless) number, unlike the correlation coefficient, coefficient of variation and index number.
✓Final answerArithmetic mean.
- AHSEC Assam Higher Secondary 1st Year Class 11 (Commerce) 2025Set ANNUAL1 markMCQQ.The algebraic sum of the deviations of a set of n values from their arithmetic mean is always __________.(a) 1(b) n(c) 0(d) infinity
›Reveal solutionSolution
Correct option: 0.
The algebraic sum of the deviations of a set of n values from their arithmetic mean is always ___. the algebraic sum of the deviations of values from their arithmetic mean is always zero.
✓Final answer0.
- AHSEC Assam Higher Secondary 1st Year Class 11 (Commerce) 2025Set ANNUAL1 markMCQQ.Which of the following measures can be calculated using ogive?(a) Mode(b) Mean(c) Median(d) All of these
›Reveal solutionSolution
Correct option: Median.
Which measure can be calculated using an ogive? the median can be obtained graphically from the ogive (cumulative frequency curve).
✓Final answerMedian.
- AHSEC Assam Higher Secondary 1st Year Class 11 (Commerce) 2025Set ANNUAL1 markMCQQ.Median divides the whole series into __________ equal parts.(a) two(b) three(c) four(d) hundred
›Reveal solutionSolution
Correct option: two.
Median divides the whole series into ___ equal parts. the median divides the whole series into two equal parts.
✓Final answertwo.
- AHSEC Assam Higher Secondary 1st Year Class 11 (Commerce) 2024Set ANNUAL1 markQ.Find out the arithmetic mean from the following data: 3, 5, 7, 9, 11
›Reveal solutionSolution
Mean = 7.
Arithmetic mean X̄ = ΣX ÷ N = (3 + 5 + 7 + 9 + 11) ÷ 5 = 35 ÷ 5 = 7.
✓Final answerArithmetic mean = 7.
- AHSEC Assam Higher Secondary 1st Year Class 11 (Commerce) 2024Set ANNUAL1 markQ.State one advantage of median.
›Reveal solutionSolution
Unaffected by extreme values.
An advantage of the median is that it is not affected by extreme values in the data — it depends only on the middle item(s), so it gives a good central value for skewed distributions; it can also be determined for open-ended classes and graphically.
✓Final answerThe median is not affected by extreme values (so it suits skewed data and open-ended distributions).
- AHSEC Assam Higher Secondary 1st Year Class 11 (Commerce) 2023Set ANNUAL1 markMCQQ.Which of the following is a measure of central tendency? (Choose the correct option)(a) Arithmetic mean(b) Median(c) Mode(d) All of the above
›Reveal solutionSolution
Correct option: (d) All of the above.
Measures of central tendency are the single representative values around which the data cluster. The arithmetic mean, the median and the mode are all measures of central tendency. Hence the correct answer is all of the above.
✓Final answer(d) All of the above (arithmetic mean, median and mode).
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