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Scientific Skills - Evaluation of Scientific Evidence

Grade 10IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Reliability: The consistency of experimental results when trials are repeated. Reliability is increased by conducting multiple trials and calculating a mean (xˉ\bar{x}).

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Validity: The extent to which an experiment measures what it is intended to measure. It depends on whether the variables are correctly controlled so that the independent variable is the only factor affecting the dependent variable.

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Precision: How close independent measurements are to each other. High precision is indicated by a small range in repeated measurements.

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Accuracy: How close a measured value is to the true or accepted value. Accuracy is often assessed by calculating the percentage error.

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Random Errors: Unpredictable fluctuations in measurements caused by human error or environmental changes. These can be minimized by repeating trials and averaging results.

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Systematic Errors: Consistent errors in one direction (always too high or always too low), usually caused by poorly calibrated equipment (e.g., a 'zero error' on a scale).

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Anomalies (Outliers): Data points that do not fit the established pattern or trend. These should be investigated and often excluded from mean calculations if the cause is known.

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Percentage Uncertainty: A way to express the precision of a measurement relative to its size, calculated as Absolute UncertaintyMeasured Value×100%\frac{\text{Absolute Uncertainty}}{\text{Measured Value}} \times 100\%.

📐Formulae

Percentage Error=∣Experimental Value−Accepted Value∣Accepted Value×100%\text{Percentage Error} = \frac{|\text{Experimental Value} - \text{Accepted Value}|}{\text{Accepted Value}} \times 100\%

Mean(xˉ)=∑i=1nxin\text{Mean} (\bar{x}) = \frac{\sum_{i=1}^{n} x_i}{n}

Percentage Uncertainty=Δxx×100%\text{Percentage Uncertainty} = \frac{\Delta x}{x} \times 100\%

Range=xmax−xmin\text{Range} = x_{max} - x_{min}

💡Examples

Problem 1:

A student conducts an experiment to determine the acceleration due to gravity (gg). They obtain a value of 9.45 m/s29.45\ m/s^2. Given that the accepted value is 9.81 m/s29.81\ m/s^2, calculate the percentage error of the experiment.

Solution:

Percentage Error=∣9.45−9.81∣9.81×100%≈3.67%\text{Percentage Error} = \frac{|9.45 - 9.81|}{9.81} \times 100\% \approx 3.67\%

Explanation:

The absolute difference between the experimental and theoretical value is divided by the theoretical value and multiplied by 100100 to find the deviation percentage.

Problem 2:

During an experiment measuring the volume of CO2CO_2 gas produced, a student records the following four trials: 24.1 cm324.1\ cm^3, 23.9 cm323.9\ cm^3, 31.5 cm331.5\ cm^3, and 24.2 cm324.2\ cm^3. Identify the anomaly and calculate the refined mean.

Solution:

Anomaly: 31.5 cm331.5\ cm^3. Refined Mean: xˉ=24.1+23.9+24.23=24.07 cm3\bar{x} = \frac{24.1 + 23.9 + 24.2}{3} = 24.07\ cm^3

Explanation:

The value 31.5 cm331.5\ cm^3 is significantly higher than the other closely clustered results, indicating an anomaly. It is excluded from the mean calculation to ensure the result is more representative of the true trend.

Problem 3:

A digital balance has an absolute uncertainty of ±0.01 g\pm 0.01\ g. If a student weighs a sample of NaClNaCl and records a mass of 2.50 g2.50\ g, what is the percentage uncertainty of this measurement?

Solution:

Percentage Uncertainty=0.012.50×100%=0.4%\text{Percentage Uncertainty} = \frac{0.01}{2.50} \times 100\% = 0.4\%

Explanation:

Percentage uncertainty is calculated by dividing the absolute uncertainty of the instrument by the measured value and expressing it as a percentage.

Evaluation of Scientific Evidence - Revision Notes & Key Formulas | IB Grade 10 Science