Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm. The relative error in the measurement of average length of the rod is:

Given: The measured lengths are 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm. Find: The relative error in the measurement of average length of the rod. Relative error is the ratio of the mean absolute error to the mean value of the measurement. Use: L = Lin L = |Li - L|n Relative error = L L Now, L = 20.00 + 19.75 + 17.01 + 18.254 = 75.014 18.75 cm Absolute errors are: |20.00 - 18.75| = 1.25 |19.75 - 18.75| = 1.00 |17.01 - 18.75| = 1.74 |18.25 - 18.75| = 0.50 Therefore, L = 1.25 + 1.00 + 1.74 + 0.504 = 4.494 1.12 Hence, Relative error = 1.1218.75 0.0597 0.06 Therefore, the relative error is 0.06. The correct option is B.

Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 1… — Solution | JEE Physics

MCQEasyJEE 2026Significant Figures & Error Analysis

Four persons measure the length of a rod as $20.00 \, \text{cm}$ , $19.75 \, \text{cm}$ , $17.01 \, \text{cm}$ and $18.25 \, \text{cm}$ . The relative error in the measurement of average length of the rod is :

A
$0.24$
B
$0.06$
C
$0.18$
D
$0.08$

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: The measured lengths are $20.00 \, \text{cm}$ , $19.75 \, \text{cm}$ , $17.01 \, \text{cm}$ and $18.25 \, \text{cm}$ .

Find: The relative error in the measurement of average length of the rod.

Relative error is the ratio of the mean absolute error to the mean value of the measurement.

Use:

\bar{L} = \frac{\sum L_i}{n}

\Delta \bar{L} = \frac{\sum |L_i - \bar{L}|}{n}

\text{Relative error} = \frac{\Delta \bar{L}}{\bar{L}}

Now,

\bar{L} = \frac{20.00 + 19.75 + 17.01 + 18.25}{4} = \frac{75.01}{4} \approx 18.75 \, \text{cm}

Absolute errors are:

|20.00 - 18.75| = 1.25

|19.75 - 18.75| = 1.00

|17.01 - 18.75| = 1.74

|18.25 - 18.75| = 0.50

Therefore,

\Delta \bar{L} = \frac{1.25 + 1.00 + 1.74 + 0.50}{4} = \frac{4.49}{4} \approx 1.12

Hence,

\text{Relative error} = \frac{1.12}{18.75} \approx 0.0597 \approx 0.06

Therefore, the relative error is $0.06$ . The correct option is B.

Common mistakes

Using the largest absolute error instead of the mean absolute error is incorrect here. The question asks for relative error in the average measurement, so first calculate the mean value and then average all absolute deviations from that mean.
Dividing by the wrong quantity gives an incorrect relative error. After finding the mean absolute error, divide it by the mean length $\bar{L}$ , not by the number of observations again or by one of the measured values.
Confusing relative error with percentage error leads to a wrong option. Relative error is dimensionless, while percentage error would be obtained only after multiplying the relative error by $100$ .

Practice more Significant Figures & Error Analysis questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trial More on Significant Figures & Error Analysis

Answer

Step-by-step solution

Common mistakes

Practice more Significant Figures & Error Analysis questions

Related questions