Скачать или смотреть Class 11 Ch#1 Physics & measurement Example 1.2 , 1.3 & 1.4 numerical new physics book Sindh part6

Class 11 Ch#1 Physics & measurement Example 1.2 1.3 & 1.4 numerical new physics book Sindh part6

Chapter 1 Physics & Measurement
Part 1
Part 2
Part 3
Part 4
Part 5
Part 6

. Random Error: Random error, also known as “chance error” or “noise,” refers to the variability in measurements that occurs due to factors that are unpredictable and uncontrollable. These factors might include fluctuations in environmental conditions, measurement instrument limitations, and human errors. Random errors affect individual measurements differently, causing them to deviate from the true value in a random manner. They tend to cancel out when averaging multiple measurements.
2. Systematic Error: Systematic error refers to consistent deviations from the true value in the same direction for all measurements. Unlike random errors, systematic errors are consistent and predictable. They can arise from flaws in experimental setup, calibration issues, or biases introduced by the experimenter. Systematic errors can’t be reduced by simply taking more measurements; they require identifying and correcting the underlying cause.
3. Random Uncertainties: Random uncertainties, also known as “uncertainty of measurement” or “precision,” quantify the extent of random errors in a set of measurements. They provide an estimate of the variability of results due to random factors. Random uncertainties are often expressed as standard deviations or standard errors, indicating how much individual measurements vary from the mean.

Formulas:

• Random Uncertainty (Standard Deviation): If you have a set of measurements {x1, x2, …, xn}, the standard deviation (s) can be calculated using the formula:

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Where xi represents individual measurements, x̄ is the mean of the measurements, and n is the number of measurements.
• Systematic Error: Systematic errors don’t have a direct formula, as they stem from consistent biases in the measurement process. Identifying and correcting systematic errors involve evaluating the experimental setup and identifying sources of bias.
• Total Uncertainty: The total uncertainty of a measurement combines both random and systematic uncertainties. It’s often expressed as the sum of the squares of these uncertainties:

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Where Δx_rand represents the random uncertainty and Δx_sys represents the systematic uncertainty.

Remember, accurate and precise measurements involve minimizing both random and systematic errors while accounting for their effects in the final results.