IIT JEE Test Series — Practice smarter, perform stronger.

Error formulas

Master Error through 21 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

Practise these formulas Know more about IIT JEE

Back to Formula Book

Error, every formula

21 formulas, typeset and free. Print it, or keep it open beside your practice.

Mean value
$a_{m e an} = \frac{1}{n} i = 1 \sum n a_{i}$
Absolute error
$Δ a_{i} = ∣ a_{m e an} - a_{i} ∣$
Mean absolute error
$Δ a_{m e an} = \frac{1}{n} i = 1 \sum n ∣Δ a_{i} ∣$
Q1MCQMean absolute error
The mean absolute error is:
- A
  $\dfrac{1}{n}\sum|\Delta a_i|$
- B
  $\sum\Delta a_i$
- C
  $\dfrac{\Delta a}{a}$
- D
  $\max\Delta a_i$
Relative error
$rel. error = \frac{Δ a _{m e an}}{a _{m e an}}$
Percentage error
$δ a = \frac{Δ a _{m e an}}{a _{m e an}} \times 100%$
Error in a sum
$Z = A + B \Rightarrow Δ Z = Δ A + Δ B$
Error in a difference
$Z = A - B \Rightarrow Δ Z = Δ A + Δ B$
Error in a product
$Z = A B \Rightarrow \frac{Δ Z}{Z} = \frac{Δ A}{A} + \frac{Δ B}{B}$
Q1MCQError in product
For $Z=AB$, the relative error is:
- A
  $\dfrac{\Delta A}{A}+\dfrac{\Delta B}{B}$
- B
  $\dfrac{\Delta A}{A}-\dfrac{\Delta B}{B}$
- C
  $\Delta A+\Delta B$
- D
  $\dfrac{\Delta A}{A}\cdot\dfrac{\Delta B}{B}$
Error in a quotient
$Z = \frac{A}{B} \Rightarrow \frac{Δ Z}{Z} = \frac{Δ A}{A} + \frac{Δ B}{B}$
Q1MCQError in quotient
For $Z=\dfrac{A}{B}$, the relative error is:
- A
  $\dfrac{\Delta A}{A}+\dfrac{\Delta B}{B}$
- B
  $\dfrac{\Delta A}{A}-\dfrac{\Delta B}{B}$
- C
  $\dfrac{\Delta A}{B}$
- D
  $\Delta A-\Delta B$
Error in a power
$Z = A^{n} \Rightarrow \frac{Δ Z}{Z} = n \frac{Δ A}{A}$
Q1MCQError in power
For $Z=A^{3}$, the relative error is:
- A
  $3\dfrac{\Delta A}{A}$
- B
  $\dfrac{\Delta A}{A}$
- C
  $\dfrac{1}{3}\dfrac{\Delta A}{A}$
- D
  $3\Delta A$
General combination
$Z = \frac{A ^{a} B ^{b}}{C ^{c}} \Rightarrow \frac{Δ Z}{Z} = a \frac{Δ A}{A} + b \frac{Δ B}{B} + c \frac{Δ C}{C}$
Least count error
$Δ a = least count of the instrument$
Q1MCQLeast count error
The least count error of an instrument equals:
- A
  its least count
- B
  half its range
- C
  zero
- D
  its full scale
Max permissible error
$Δ a = place value of the last digit$
Q1MCQMax permissible error
When nothing is stated, the maximum permissible error is:
- A
  the place value of the last digit
- B
  $1\%$
- C
  zero
- D
  half the reading
Systematic error
$consistent bias (miscalibration, procedure)$
Q1MCQSystematic error
A systematic error is characterised by:
- A
  a consistent bias in one direction
- B
  random scatter
- C
  no fixed sign
- D
  averaging to zero
Random error
$scatter from fluctuations; reduced by averaging$
Q1MCQRandom error
Random errors can be reduced by:
- A
  taking the average of many readings
- B
  recalibrating once
- C
  using a bias
- D
  nothing
Precision
$small random error \Rightarrow high precision$
Q1MCQPrecision
A measurement with small random error is said to have high:
- A
  precision
- B
  accuracy
- C
  bias
- D
  range
Accuracy
$small random + systematic error \Rightarrow high accuracy$
Q1MCQAccuracy
A measurement with small random AND systematic error has high:
- A
  accuracy
- B
  precision only
- C
  bias
- D
  least count
Sig. figs (nonzero digits)
$all nonzero digits are significant$
Sig. figs (multiplication)
$result has the least number of significant figures$
Q1MCQSig figs multiplication
When multiplying, the result keeps:
- A
  the least number of significant figures
- B
  the most significant figures
- C
  the least decimal places
- D
  all digits
Sig. figs (addition)
$result has the least number of decimal places$
Q1MCQSig figs addition
When adding, the result keeps:
- A
  the least number of decimal places
- B
  the least significant figures
- C
  the most decimal places
- D
  all digits
Error interval
$a \in (a_{m e an} - Δ a, a_{m e an} + Δ a)$
Q1MCQError interval
A measurement $a_{mean}\pm\Delta a$ means the true value lies in:
- A
  $(a_{mean}-\Delta a,\ a_{mean}+\Delta a)$
- B
  $(0,\ a_{mean})$
- C
  $(a_{mean},\ \infty)$
- D
  exactly $a_{mean}$

Other ways to revise this chapter

Master this chapter with similar other learning materials.

Preparing students for India’s top institutes

Our students are currently into top technological and medical institutes of India.

IIT Bombay
IIT Delhi
IIT Madras
IIT Kanpur
IIT Kharagpur
IIT Roorkee
IIT Guwahati
IIT BHU Varanasi
AIIMS Delhi
NIT Tiruchirappalli
NIT Rourkela
IIT Bombay
IIT Delhi
IIT Madras
IIT Kanpur
IIT Kharagpur
IIT Roorkee
IIT Guwahati
IIT BHU Varanasi
AIIMS Delhi
NIT Tiruchirappalli
NIT Rourkela

Join QuestPix, Today!

Get notified first, with exam & curriculum updates, course & test series launch offers, motivation & success stories and free learning resources recommended by toppers.

Error formulas

Error, every formula

Mean value

Absolute error

Mean absolute error

Relative error

Percentage error

Error in a sum

Error in a difference

Error in a product

Error in a quotient

Error in a power

General combination

Least count error

Max permissible error

Systematic error

Random error

Precision

Accuracy

Sig. figs (nonzero digits)

Sig. figs (multiplication)

Sig. figs (addition)

Error interval

More JEE Advanced Physics formula sheets

Other ways to revise this chapter

Preparing students for India’s top institutes

Join QuestPix, Today!