Class 11 Economics Formula Sheet 2026-27 (Free PDF): Statistics and Microeconomics

Every formula from the Statistics and Microeconomics NCERT Class 11 Economics chapters in one place, checked against the NCERT textbook (Reprint 2026-27) and the official CBSE 2026-27 syllabus. Mean, median, mode, correlation and index numbers, plus elasticity, costs, revenue and market equilibrium.

How to use this sheet. The CBSE 2026-27 Class 11 Economics paper has two parts: Statistics for Economics (Part A) and Introductory Microeconomics (Part B). This sheet collects every formula from both NCERT books. Chapters without formulas are left out. Chapter numbers match each NCERT book. The amber box marked ★ Syllabus only covers a topic the 2026-27 syllabus lists but the current NCERT reprint does not print. It uses the standard method. Grey boxes marked ◇ Not in 2026-27 syllabus are in the NCERT books but not in the current syllabus. They are kept for reference.

Statistics 3: Organisation of Data
Statistics 5: Measures of Central Tendency
Statistics 6: Correlation
Statistics 7: Index Numbers
Micro 1: Introduction
Micro 2: Theory of Consumer Behaviour
Micro 3: Production and Costs
Micro 4: The Theory of the Firm under Perfect Competition
Micro 5: Market Equilibrium

S3Organisation of Data

Frequency distribution

$$\text{Class mark (mid-point)} = \frac{\text{Upper class limit} + \text{Lower class limit}}{2}$$
Class interval (width) $=$ Upper class limit $-$ Lower class limit
Range $=$ Largest value $-$ Smallest value

Inclusive to exclusive (adjusted limits)

Adjustment $= \dfrac{\text{Lower limit of next class} - \text{Upper limit of this class}}{2}$ (usually 0.5)
Adjusted lower limit $=$ lower limit $-$ adjustment; adjusted upper limit $=$ upper limit $+$ adjustment
Adjusted class mark $= \dfrac{\text{Adjusted upper limit} + \text{Adjusted lower limit}}{2}$

S5Measures of Central Tendency

Arithmetic mean

Method	Individual series	Discrete / continuous (use mid-points $m$)
Direct	$\bar{X} = \dfrac{\Sigma X}{N}$	$\bar{X} = \dfrac{\Sigma fX}{\Sigma f}$ or $\dfrac{\Sigma fm}{\Sigma f}$
Assumed mean ($d = X - A$)	$\bar{X} = A + \dfrac{\Sigma d}{N}$	$\bar{X} = A + \dfrac{\Sigma fd}{\Sigma f}$
Step deviation ($d' = \frac{X - A}{c}$)	$\bar{X} = A + \dfrac{\Sigma d'}{N} \times c$	$\bar{X} = A + \dfrac{\Sigma fd'}{\Sigma f} \times c$

Sum of deviations from the mean is zero: $\Sigma(X - \bar{X}) = 0$
Weighted mean: $$\bar{X}_w = \frac{\Sigma WX}{\Sigma W} = \frac{W_1X_1 + W_2X_2 + \dots}{W_1 + W_2 + \dots}$$

Median

Individual and discrete series: Median $=$ size of the $\left(\dfrac{N+1}{2}\right)^{\text{th}}$ item (arrange in order; use cumulative frequency for discrete)
Continuous series: median class holds the $\left(\dfrac{N}{2}\right)^{\text{th}}$ item $$\text{Median} = L + \frac{\frac{N}{2} - c.f.}{f} \times h$$
$L$ lower limit of median class, $c.f.$ cumulative frequency of the class before it, $f$ its frequency, $h$ its width

Mode

Most frequent value; data can be unimodal, bimodal or multimodal
Continuous series (modal class = highest frequency): $$\text{Mode} = L + \frac{D_1}{D_1 + D_2} \times h$$
$D_1 = f_{\text{modal}} - f_{\text{before}}$, $\ D_2 = f_{\text{modal}} - f_{\text{after}}$ (ignore signs); classes must be equal and exclusive
Median always lies between mean and mode: Mean > Median > Mode, or Mean < Median < Mode

Quartiles and percentiles

$Q_1 =$ size of $\left(\dfrac{N+1}{4}\right)^{\text{th}}$ item; $\ Q_3 =$ size of $\left(\dfrac{3(N+1)}{4}\right)^{\text{th}}$ item
Percentiles split data into 100 equal parts; the 50th percentile is the median

S6Correlation

Karl Pearson's coefficient (product moment)

With deviations $x = X - \bar{X}$, $y = Y - \bar{Y}$: $$\text{Cov}(X,Y) = \frac{\Sigma xy}{N}, \qquad r = \frac{\Sigma xy}{N\sigma_x\sigma_y} = \frac{\Sigma(X - \bar{X})(Y - \bar{Y})}{\sqrt{\Sigma(X - \bar{X})^2}\sqrt{\Sigma(Y - \bar{Y})^2}}$$

Direct (actual values): $$r = \frac{N\Sigma XY - (\Sigma X)(\Sigma Y)}{\sqrt{N\Sigma X^2 - (\Sigma X)^2}\,\sqrt{N\Sigma Y^2 - (\Sigma Y)^2}}$$

Step deviation: put $U = \frac{X - A}{B}$, $V = \frac{Y - C}{D}$ and compute $r$ from $U, V$; $r_{UV} = r_{XY}$ because $r$ is unaffected by change of origin and scale.

Properties of r

$-1 \le r \le 1$; a value outside this range means a calculation error
No unit; unaffected by change of origin and scale
$r = +1$ or $-1$: perfect correlation; $r = 0$: no linear relation (variables may still be related non-linearly)
Correlation shows covariation, not causation

Spearman's rank correlation

Ranks not repeated: $$r_s = 1 - \frac{6\Sigma D^2}{n(n^2 - 1)} = 1 - \frac{6\Sigma D^2}{n^3 - n}$$
Ranks repeated (each tie of $m$ items gets the average rank): $$r_s = 1 - \frac{6\left[\Sigma D^2 + \dfrac{m_1^3 - m_1}{12} + \dfrac{m_2^3 - m_2}{12} + \dots\right]}{n(n^2 - 1)}$$
$D$ = difference between the two ranks of an item; $\Sigma D = 0$ is a check

S7Index Numbers

Simple aggregative price index

$$P_{01} = \frac{\Sigma P_1}{\Sigma P_0} \times 100$$
$P_1$ current period price, $P_0$ base period price; base year index $= 100$
Index 138.5 means prices rose 38.5% over the base period
Unweighted: every item counts equally, whatever its importance.

Inflation and uses of CPI

$$\text{Inflation rate} = \frac{X_t - X_{t-1}}{X_{t-1}} \times 100$$ ($X$ = WPI or CPI for periods $t$ and $t-1$)
Purchasing power of money $= \dfrac{1}{\text{Cost of living index}}$
Real wage $= \dfrac{\text{Money wage}}{\text{Cost of living index}} \times 100$
Types: WPI (wholesale prices), CPI (retail, cost of living), IIP (industrial production)

Weighted and averaging-of-relatives methods

Laspeyres (base quantities): $P_{01} = \dfrac{\Sigma P_1q_0}{\Sigma P_0q_0} \times 100$; Paasche (current quantities): $P_{01} = \dfrac{\Sigma P_1q_1}{\Sigma P_0q_1} \times 100$
Simple average of price relatives: $P_{01} = \dfrac{1}{n}\Sigma\dfrac{P_1}{P_0} \times 100$; weighted: $P_{01} = \dfrac{\Sigma W\left(\frac{P_1}{P_0} \times 100\right)}{\Sigma W}$
CPI by the weighted relatives method: $\text{CPI} = \dfrac{\Sigma WR}{\Sigma W}$, $R = \dfrac{P_1}{P_0} \times 100$

M1Introduction (Microeconomics)

Production possibility frontier and opportunity cost

PPF: all combinations of two goods an economy can produce with given resources and technology, using them fully and efficiently
Opportunity cost of one more unit of a good $=$ amount of the other good given up: $$\text{Marginal opportunity cost} = \frac{\text{Units of } Y \text{ given up}}{\text{Extra units of } X \text{ gained}} = \left|\frac{\Delta Y}{\Delta X}\right|$$
Point inside the PPF: resources unemployed or used wastefully. Outward shift: more resources or better technology
Central problems: what, how and for whom to produce. Positive economics = what is; normative = what ought to be

M2Theory of Consumer Behaviour

Utility

$$MU_n = TU_n - TU_{n-1}, \qquad TU_n = MU_1 + MU_2 + \dots + MU_n$$
Law of diminishing marginal utility: each extra unit adds less utility
TU is maximum when $MU = 0$; TU falls when MU is negative

Consumer's equilibrium by marginal utility

One good: $\dfrac{MU_x}{P_x} = MU_m$ (marginal utility of a rupee); buy until MU (in rupees) $= P_x$
Two goods: $$\frac{MU_x}{P_x} = \frac{MU_y}{P_y} = MU_m$$ and MU falls as consumption rises

Budget set and budget line

Budget set: $p_1x_1 + p_2x_2 \le M$; budget line: $p_1x_1 + p_2x_2 = M$
$$x_2 = \frac{M}{p_2} - \frac{p_1}{p_2}x_1$$
Intercepts $\dfrac{M}{p_1}$ (horizontal) and $\dfrac{M}{p_2}$ (vertical); slope $= -\dfrac{p_1}{p_2}$
Income change: parallel shift. Price change of one good: the line rotates about the other intercept

Indifference curves and equilibrium

$$MRS = \left|\frac{\Delta x_2}{\Delta x_1}\right|$$ (amount of good 2 given up for one more unit of good 1); diminishing MRS makes the IC convex
Optimum: budget line tangent to the highest IC: $$MRS = \frac{p_1}{p_2}$$
ICs slope down, never intersect; a higher IC gives higher utility (monotonic preferences)

Demand

Demand function $q = d(p)$; linear: $d(p) = a - bp$ for $0 \le p \le \frac{a}{b}$
Market demand $=$ horizontal sum of individual demands
Change in own price: movement along the curve. Change in income, prices of related goods, tastes: shift of the curve
Normal good: demand rises with income; inferior: falls. Substitutes: $p_y \uparrow \Rightarrow d_x \uparrow$; complements: $p_y \uparrow \Rightarrow d_x \downarrow$

Price elasticity of demand

Percentage method: $$e_D = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}} = \frac{\Delta Q / Q}{\Delta P / P} = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q}$$
$\%$ change in quantity $= \dfrac{Q_2 - Q_1}{Q_1} \times 100$; $e_D$ is negative (law of demand), so compare $|e_D|$
$|e_D| > 1$ elastic; $= 1$ unitary; $< 1$ inelastic; $0$ perfectly inelastic (vertical curve); $\infty$ perfectly elastic (horizontal)

Total expenditure method ($E = p \times q$)	Price falls	Price rises
Elastic $\|e_D\| > 1$	Expenditure rises	Expenditure falls
Unitary $\|e_D\| = 1$	Unchanged	Unchanged
Inelastic $\|e_D\| < 1$	Expenditure falls	Expenditure rises

Factors: availability of close substitutes (more elastic), necessity vs luxury (necessities inelastic, luxuries elastic).

Geometric method on a straight-line demand curve

For $q = a - bp$: $e_D = -b\dfrac{p}{q}$; at a point, $|e_D| = \dfrac{\text{lower segment}}{\text{upper segment}}$
$e_D = 0$ at the quantity axis, $|e_D| = 1$ at the midpoint, $\infty$ at the price axis
Rectangular hyperbola $pq = $ constant: $|e_D| = 1$ everywhere

M3Production and Costs

Product of labour (short run, capital fixed)

Production function $q = f(L, K)$
$$AP_L = \frac{TP_L}{L}, \qquad MP_L = \frac{\Delta TP}{\Delta L} = TP_L - TP_{L-1}$$
$TP = \Sigma MP$. MP rises then falls (law of variable proportions / diminishing marginal product)
$MP > AP$: AP rising; $MP = AP$: AP at maximum; $MP < AP$: AP falling. TP maximum when $MP = 0$

Short-run costs

$$TC = TFC + TVC$$
$AFC = \dfrac{TFC}{q}$, $\ AVC = \dfrac{TVC}{q}$, $\ SAC = \dfrac{TC}{q} = AVC + AFC$
$$SMC = \frac{\Delta TC}{\Delta q} = TC_q - TC_{q-1}$$ (= change in TVC, since TFC is fixed); $TVC = \Sigma SMC$
AFC falls continuously (rectangular hyperbola); AVC, SAC and SMC are U-shaped
SMC cuts AVC and SAC at their minimum points; min AVC comes before min SAC

Returns to scale and long-run costs

Constant returns: $f(tx_1, tx_2) = t\,f(x_1, x_2)$; increasing: $> t\,f$; decreasing: $< t\,f$
Cobb-Douglas $q = x_1^{\alpha}x_2^{\beta}$: CRS if $\alpha + \beta = 1$, IRS if $> 1$, DRS if $< 1$
$LRAC = \dfrac{TC}{q}$, $\ LRMC = TC_{q} - TC_{q-1}$; isoquants join input combinations giving the same output

M4The Theory of the Firm under Perfect Competition

Revenue

$$TR = p \times q, \qquad AR = \frac{TR}{q} = p, \qquad MR = \frac{\Delta TR}{\Delta q}$$
Perfect competition (price taker): $MR = AR = p$; TR is a straight line through the origin with slope $p$
Features: many buyers and sellers, homogeneous product, free entry and exit, perfect information

Producer's equilibrium (profit maximisation)

Profit $\pi = TR - TC$
Condition 1: $MR = MC$, i.e. $p = MC$
Condition 2: MC is non-decreasing (rising) at that output
Condition 3 (short run): $p \ge AVC$, otherwise shut down

Supply curve of a firm

Short-run supply curve: rising part of SMC at and above min AVC; zero output below it
Shut-down point (short run): $p = \min AVC$
Break-even point (normal profit, zero economic profit): $p = \min AC$
Shifts: technological progress (right), rise in input prices (left), unit tax (left)
Market supply $=$ horizontal sum of firms' supplies

Price elasticity of supply

$$e_S = \frac{\%\ \text{change in quantity supplied}}{\%\ \text{change in price}} = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q}$$
$e_S$ is positive; vertical supply curve: $e_S = 0$
Straight-line supply curve through the origin: $e_S = 1$; cutting the price axis: $e_S > 1$; cutting the quantity axis: $e_S < 1$.

Long run

Long-run conditions: $p = LRMC$, LRMC non-decreasing, $p \ge LRAC$; long-run supply curve = rising LRMC above min LRAC

M5Market Equilibrium

Equilibrium (fixed number of firms)

$$q^D(p^*) = q^S(p^*)$$
Excess demand $ED(p) = q^D - q^S > 0$ below $p^*$ (price rises); excess supply $ES(p) = q^S - q^D > 0$ above $p^*$ (price falls)
Example: $q^D = 200 - p$, $q^S = 120 + p$ gives $p^* = 40$, $q^* = 160$

Shifts in demand and supply

Change	$p^*$	$q^*$
Demand rises (shifts right)	↑	↑
Demand falls	↓	↓
Supply rises (shifts right)	↓	↑
Supply falls	↑	↓
Both rise	?	↑
Demand rises, supply falls	↑	?

"?" depends on which shift is bigger.

Price ceiling and price floor

Price ceiling: maximum price set below equilibrium (e.g. wheat, rice, kerosene) ⇒ excess demand, rationing (ration shops), possible black market
Price floor: minimum price set above equilibrium (e.g. minimum support price, minimum wage) ⇒ excess supply; government buys the surplus (buffer stocks)

Free entry and exit; labour market

Free entry and exit: $p_0 = \min AC$; number of firms $n_0 = \dfrac{q^D(p_0)}{q_{0f}}$ (market quantity / one firm's supply)
Labour demand: firm hires until $w = VMP_L = p \times MP_L$ ($MRP_L = MR \times MP_L$)

Method	Individual series	Discrete / continuous (use mid-points \(m\))
Direct	\(\bar{X} = \dfrac{\Sigma X}{N}\)	\(\bar{X} = \dfrac{\Sigma fX}{\Sigma f}\) or \(\dfrac{\Sigma fm}{\Sigma f}\)
Assumed mean (\(d = X - A\))	\(\bar{X} = A + \dfrac{\Sigma d}{N}\)	\(\bar{X} = A + \dfrac{\Sigma fd}{\Sigma f}\)
Step deviation (\(d' = \frac{X - A}{c}\))	\(\bar{X} = A + \dfrac{\Sigma d'}{N} \times c\)	\(\bar{X} = A + \dfrac{\Sigma fd'}{\Sigma f} \times c\)