Experimental Methods and Data Analysis

<p>Inconsistent scales. (B)</p> Signup and view all the answers

<p>A curve. (A)</p> Signup and view all the answers

<p>Understanding and filtering data effectively. (B)</p> Signup and view all the answers

<p>Calibration. (C)</p> Signup and view all the answers

<p>Three-dimensional bar charts. (A)</p> Signup and view all the answers

<p>They can overfit the data. (B)</p> Signup and view all the answers

<p>fminsearch (D)</p> Signup and view all the answers

<p>The difference between the model fit and observed values. (B)</p> Signup and view all the answers

<p>A higher R-squared generally indicates a better fit. (D)</p> Signup and view all the answers

<p>Desired quantity. (B)</p> Signup and view all the answers

<p>Insight into the degree of fit. (A)</p> Signup and view all the answers

<p>Polynomial fits using least-squares algorithms. (B)</p> Signup and view all the answers

<p>It perfectly fits the data points. (D)</p> Signup and view all the answers

<p>Removing trends to analyze the remaining components. (D)</p> Signup and view all the answers

<p>The summed square deviations of actual values from their mean. (D)</p> Signup and view all the answers

<p>Mean (D)</p> Signup and view all the answers

<p>Second central moment (D)</p> Signup and view all the answers

<p>The alignment of data relative to the mean (D)</p> Signup and view all the answers

<p>It has a value of zero for a normal distribution (D)</p> Signup and view all the answers

<p>To minimize the sum of squared distances (B)</p> Signup and view all the answers

<p>$\frac{1}{N \sigma^3} \sum (X_i - \bar{X})^3$ (B)</p> Signup and view all the answers

<p>Cumulative moments (C)</p> Signup and view all the answers

<p>A longer tail on the left side of the distribution (B)</p> Signup and view all the answers

<p>The sharpness of the peak of the distribution (B)</p> Signup and view all the answers

<p>Partial derivatives (A)</p> Signup and view all the answers

<p>Standard deviation (D)</p> Signup and view all the answers

<p>They can lead to overfitting (A)</p> Signup and view all the answers

<p>Mean squared value of data (C)</p> Signup and view all the answers

<p>It has a sharper peak compared to a normal distribution (C)</p> Signup and view all the answers

<p>6.7 (D)</p> Signup and view all the answers

<p>It reduces the error. (C)</p> Signup and view all the answers

<p>The only difference between measurements is noise. (C)</p> Signup and view all the answers

<p>A measure of the power contained in an oscillating signal. (B)</p> Signup and view all the answers

<p>It introduces a delay in the measurement. (C)</p> Signup and view all the answers

<p>They must be sorted in ascending order. (C)</p> Signup and view all the answers

<p>Calculating a mean for each block of samples. (A)</p> Signup and view all the answers

<p>It can distort the average value. (C)</p> Signup and view all the answers

<p>It is similar to a moving average but applies a different calculation. (C)</p> Signup and view all the answers

<p>It can result in a better approximation of the mean. (A)</p> Signup and view all the answers

<p>The least precise measurement used in the calculation. (C)</p> Signup and view all the answers

<p>Averaging and convolution. (B)</p> Signup and view all the answers

<p>$X_t = A sin(ωt)$ (C)</p> Signup and view all the answers

<p>To minimize the effect of random noise. (C)</p> Signup and view all the answers

Graphs and tables are common methods for presenting experimental data. Units and clear structure should be used in tables. Graphs should also be clear and easy to read.

Methods for understanding collected data; includes calculating averages, applying filters, fitting curves, and calibrating data sets.

Drawing a line or a curve through plotted data points to represent a relationship that best describes the data.

The number of digits that contribute to the accuracy of a measurement or calculation; multiplication and division use the fewest significant figures in the calculation and addition and subtraction use the fewest decimal places.

Process of adjusting a measurement instrument or raw data to a known, standard value.

Measurements and observations collected from experiments.

A predictable relationship between measurements and their outcomes that can be used for predicting and designing.

Graphs that are poorly designed or presented and do not effectively convey the data.

When multiplying measured values, the result should have the same number of significant figures as the least precise measurement.

When adding measured values, the result should have the same precision (number of decimal places) as the least precise measurement.

The sum of all values divided by the number of values.

The average value of a signal over a period of time.

Averaging the results of multiple independent measurements to reduce noise.

Calculate the average of a subset of recent data points.

Calculates the middle value of a subset of recent data points.

Reducing the amount of data by averaging over blocks of measurements.

A measure of the power of a fluctuating signal, calculated by squaring the values, taking the average, and then taking the square root.

The middle value when data is sorted.

Average of the absolute deviations from the mean.

Averaging over more samples reduces the errors from noise

Signal with periodic fluctuations around a certain value

Effective value of an alternating current, or a rapidly fluctuating signal. This value is representative of the power

Polynomials with a degree greater than 2, e.g., cubic (degree 3) or quartic (degree 4).

A function in MATLAB that uses least-squares to fit data with polynomials.

Using a mathematical function of the form y = a*e^(bx) + c to represent data.

A MATLAB function for finding the minimum of a function, useful for fitting any generic function to data.

The differences between the actual data points and the values predicted by the fitted curve.

A statistical measure (between 0 and 1) that indicates how well the curve fits the data, with 1 being a perfect fit.

The sum of the squared deviations of each data point from the mean value.

The sum of the squared differences between the actual data points and the values predicted by the curve.

Removing the underlying trend from data, leaving only the fluctuations.

Moments are statistical parameters that describe the shape of data distributions. They help us understand the central tendency, spread, and asymmetry of our data.

A raw moment measures how the data points are spread around zero. The first raw moment is the mean.

A central moment measures how data points are spread around the mean. The second central moment is the variance.

A standardised moment measures the spread of data in terms of standard deviations. This allows us to compare data from different populations.

Skewness measures the asymmetry of a distribution. It tells us whether the tail of the distribution is longer on the positive or negative side of the mean.

A distribution with a longer tail on the negative side of the mean.

A distribution with a longer tail on the positive side of the mean.

Kurtosis measures the 'peakedness' or 'tailedness' of a distribution. It tells us how concentrated the data is around the mean.

A distribution with a flatter peak and broader tails than a normal distribution.

A distribution with a sharper peak and narrower tails than a normal distribution.

Curve fitting is the process of finding a mathematical function that best represents the relationship between data points.

A method of curve fitting where we find the line that minimizes the sum of the squared distances between the data points and the line.

Least squares calculates the sum of the squared distances between the data points and the fitted line, then uses calculus to minimize this sum.

A polynomial is a mathematical expression with terms containing variables raised to non-negative integer powers.

Polynomials with a degree greater than 2, e.g. cubic (degree 3), quartic (degree 4).