Errors in measurements

When measuring, there are errors and differences between measurements. How can we know which number to choose?

The central tendency of a data set:

1. Mode: the number that shows up the most
2. Average
3. Median: the number in the middle of the data set

Why central tendency is important? To give a rough representation of something

1. Precision: How close the measurements are from each other
2. Accuracy: How close is the measurement from the true value

They affect: the precision of the measurement, does the tool allow that measurement, and how certain you are with the measurement.

Check your measurement with accuracy, precision with plotting.

Measure of variance for the population:

Mean:

$$\mu =\frac{1}{n}\sum _{i=1}^n{x}_i$$

Population variance: average the squared differences Why the population variance is squared? To get rid of the negative Standard deviation: the square root of variance (on average, how far apart is the data values from the mean)

Measure of variance for the sample:

Mean: the same The difference between sample and population:

$$s=\frac{1}{1-n}\sum _{i=1}^n(x_i-x{)}^2$$