Topic 4: Accuracy, Precision & Errors

Accuracy

Accuracy refers to how close a measured value is to the true or accepted value. A measurement is said to be accurate if it is very near to the actual value.

Example: If the true length of a rod is 10 cm and the measured value is 9.9 cm, the measurement is accurate.

Precision

Precision refers to how close repeated measurements are to each other, regardless of whether they are close to the true value or not.

Example: If repeated measurements give values like 8.1 cm, 8.1 cm, and 8.1 cm, they are precise but may not be accurate.

Accuracy vs Precision

  • Accuracy → closeness to the true value
  • Precision → closeness among repeated measurements
  • A measurement can be precise but not accurate

Errors in Measurement

Error is the difference between the measured value and the true value. Errors are unavoidable and occur due to limitations of measuring instruments or human observation.

Types of Errors

  • Systematic Errors – occur due to faulty instruments or incorrect methods
  • Random Errors – occur due to unpredictable variations
  • Gross Errors – occur due to human mistakes

Reducing Errors

  • Use proper measuring instruments
  • Take multiple readings and calculate the mean
  • Handle instruments carefully
Q1. Accuracy refers to:
A) Closeness to true value
B) Closeness among readings
C) Instrument quality
D) Zero error
Answer: A

Q2. Precision means:
A) Correct value
B) True value
C) Repeated values close to each other
D) No error
Answer: C

Q3. A measurement can be:
A) Accurate but not precise
B) Precise but not accurate
C) Both accurate and precise
D) All of the above
Answer: D

Q4. Which error occurs due to faulty instruments?
A) Random error
B) Gross error
C) Systematic error
D) Human error
Answer: C

Q5. Which method helps reduce random errors?
A) Changing instrument
B) Taking mean of readings
C) Ignoring errors
D) Using old instruments
Answer: B

Accuracy, Precision & Errors – Quick Revision

  • Accuracy: Closeness of measured value to true value
  • Precision: Closeness of repeated measurements

Key Differences

  • Accuracy depends on true value
  • Precision depends on consistency

Errors

  • Error = Measured value − True value

Types of Errors

  • Systematic Error – Instrument or method related
  • Random Error – Unpredictable variations
  • Gross Error – Human mistakes

Error Reduction

  • Multiple readings
  • Proper instruments
  • Correct observation

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