Working with data

Sometimes data will be given in the form of text columns. You should be able to use a spreadsheet program to add columns together or multiply all numbers in a column by a value.

You should be able to use a plotting program to plot a function or data in tabular form. You should also be able to numerically integrate or numerically differentiate data in a column. The app, Numerical integration and differentiation will plot, differentiate, and integrate columns of data.

Sometimes the data you have uses another decimal mark than the programs on your computer use. You should know how to replace all decimal points (.) with commas (,) and all commas (,) with decimal points (.) in a table of data. The Physik-M apps always use decimal points (.) for the decimal mark. You can use the replace function of a text editor or the Decimal point ↔ Comma app.

You should be able to calculate the mean and standard deviation of a column of data. The mean value of $N$ data points is,

$\large \langle x\rangle = \frac{1}{N}\sum\limits_{i=1}^Nx_i$.

The standard deviation $\Delta x$, is the square root of the mean of the squares $\langle x^2\rangle=\frac{1}{N}\sum x_i^2$ minus the square of the mean $\langle x\rangle^2=\left(\frac{1}{N}\sum x_i\right)^2$.

$\Delta x=\sqrt{\langle x^2\rangle -\langle x\rangle^2}$.

The form below will calculate the mean and standard deviation of the column of numbers that are put in the red textbox below. Red textboxes will be used for input fields for columns of data.

To make the histogram, the interval between $x_{min}$ and $x_{max}$ was divided into 100 bins and each data point was sorted into one of those bins.