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Scientific Skills - Evaluation of Scientific Evidence

Grade 9IB

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

🔑Concepts

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Reliability: Refers to the consistency of the results. If an experiment is repeated and yields similar values with a small range (R=xmax−xminR = x_{\text{max}} - x_{\text{min}}), the data is considered reliable.

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Validity: Refers to whether the experimental method successfully measures what it intended to measure. A valid experiment must have well-controlled variables to ensure a fair test.

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Accuracy: The proximity of a measurement to the true or accepted value. Accuracy is often evaluated using the percentage error formula.

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Precision: The degree of agreement among repeated measurements. Highly precise data has very little spread around the mean value (xˉ\bar{x}).

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Random Error: Unpredictable fluctuations in measurements due to human reaction time or environmental changes. These can be minimized by calculating the mean (xˉ\bar{x}) of multiple trials.

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Systematic Error: Consistent, repeatable errors often caused by faulty equipment (e.g., zero error on a balance) or flawed experimental design. These errors affect the accuracy of the results.

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Outliers: Data points that deviate significantly from the rest of the set. These should be identified and analyzed to determine if they resulted from an error in the procedure.

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Evaluating Conclusions: A conclusion is evaluated based on whether the data supports the hypothesis, the strength of the correlation (rr), and the presence of any anomalies.

📐Formulae

Percentage Error=∣Experimental Value−Theoretical ValueTheoretical Value∣×100%\text{Percentage Error} = \left| \frac{\text{Experimental Value} - \text{Theoretical Value}}{\text{Theoretical Value}} \right| \times 100\%

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

Percentage Uncertainty=Absolute UncertaintyMeasured Value×100%\text{Percentage Uncertainty} = \frac{\text{Absolute Uncertainty}}{\text{Measured Value}} \times 100\%

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

💡Examples

Problem 1:

In an experiment to determine the acceleration due to gravity, a student calculates a value of 9.45 m/s29.45 \text{ m/s}^2. The accepted theoretical value is 9.81 m/s29.81 \text{ m/s}^2. Calculate the percentage error and identify if this indicates high accuracy.

Solution:

Percentage Error=∣9.45−9.819.81∣×100%\text{Percentage Error} = \left| \frac{9.45 - 9.81}{9.81} \right| \times 100\% Percentage Error=∣−0.369.81∣×100%≈3.67%\text{Percentage Error} = \left| \frac{-0.36}{9.81} \right| \times 100\% \approx 3.67\%

Explanation:

The percentage error is 3.67%3.67\%. Since the error is relatively low (typically less than 5%5\% is considered acceptable in school laboratories), the result can be considered reasonably accurate, though there is room for improvement in the experimental setup.

Problem 2:

A student measures the mass of a chemical sample three times: 2.45 g2.45 \text{ g}, 2.44 g2.44 \text{ g}, and 2.46 g2.46 \text{ g}. However, they later realize the electronic balance was not tared and showed 0.10 g0.10 \text{ g} when empty. Evaluate the precision and accuracy of these results.

Solution:

Range=2.46−2.44=0.02 g\text{Range} = 2.46 - 2.44 = 0.02 \text{ g} True Mean=(2.45−0.10)+(2.44−0.10)+(2.46−0.10)3=2.35 g\text{True Mean} = \frac{(2.45 - 0.10) + (2.44 - 0.10) + (2.46 - 0.10)}{3} = 2.35 \text{ g}

Explanation:

The measurements are highly precise because the range (0.02 g0.02 \text{ g}) is very small. However, the measurements are inaccurate due to a systematic error (zero error of 0.10 g0.10 \text{ g}). Every reading was consistently 0.10 g0.10 \text{ g} higher than the true value.