JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV MEASURING INSTRUMENTS Previous Question Paper (July/August - 2022 - R18)

Statistical analysis is essential in measurement to quantify the uncertainty and precision of data sets. When a measurement is repeated multiple times, the results vary due to random errors. The analysis involves calculating central tendencies and dispersion metrics.

• Arithmetic Mean (x̄): The sum of all readings divided by the number of readings.
• Deviation (d): The difference between an individual reading and the mean.
• Standard Deviation (σ): Represents the root-mean-square deviation, indicating the spread of data around the mean.
• Variance (σ²): The square of the standard deviation.

Example: Consider five voltage measurements: 100V, 102V, 98V, 101V, and 99V.

1. Mean (x̄) = (100+102+98+101+99) / 5 = 100V.
2. Deviations: 0, 2, -2, 1, -1.
3. Sum of squares of deviations = 0² + 2² + (-2)² + 1² + (-1)² = 0 + 4 + 4 + 1 + 1 = 10.
4. Standard Deviation (σ) = sqrt(10 / (5-1)) = sqrt(2.5) ≈ 1.58V.

This indicates that most readings fall within 1.58V of the mean, providing a measure of the instrument's repeatability.

To calculate the limiting error, we first determine the absolute error based on the full-scale reading and then express it as a percentage of the actual measured value.

• Full Scale Reading (FSR) = 150V
• Guaranteed Accuracy = 1% of FSR = 0.01 × 150V = 1.5V
• Measured Value (V_m) = 75V

The limiting error in percent is calculated as:

Limiting Error (%) = (Absolute Error / Measured Value) × 100
Limiting Error (%) = (1.5 / 75) × 100
Limiting Error (%) = 0.02 × 100 = 2%

Thus, the limiting error for the 75V measurement is 2%.