Statistical Evaluation for IB Biology

Mean

What is Mean?

The sum of all the data points divided by the total number of data points. In math this is called average. In statistics it is called mean.

Measure of central tendency for normally distributed data.

DO NOT calculate a mean from values that are already averages.
DO NOT calculate a mean when the measurement scale is not linear (i.e. pH units are not measured on a linear scale
For example: let 5 data points be 1, 2, 3, 4, and 5

mean= 1+2+3+4+5/5 = 15/5 = 3

WHat is Median

Central value in a set of data that is arranged in order from lowest to highest so that no more than half the values are above this number and no more than half are below
When there is an even number of values, there still a median

What is Mode?

The most frequent value in data set and it can be more than one value.
for example: In the data {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6, as it occurs most often.

Example of median:

data set (3, 13, 7, 5, 21, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29)

When we put those numbers in order we have:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56

There are fifteen numbers. Our middle is the eighth number:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56

Standard Deviation and Standard Error

What is standard deviation?

Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean. In any distribution, about 95% of values will be within 2 standard deviations of the mean.

How to Calculate the Standard Deviation:

Calculate the mean (x̅) of a set of data
Subtract the mean from each point of data to determine (x-x̅). You'll do this for each data point, so you'll have multiple (x-x̅).
Square each of the resulting numbers to determine (x-x̅)^2. As in step 2, you'll do this for each data point, so you'll have multiple (x-x̅)^2.
Add the values from the previous step together to get ∑(x-x̅)^2. Now you should be working with a single value.
Calculate (n-1) by subtracting 1 from your sample size. Your sample size is the total number of data points you collected.
Divide the answer from step 4 by the answer from step 5
Calculate the square root of your previous answer to determine the standard deviation.
Be sure your standard deviation has the same number of units as your raw data, so you may need to round your answer.
The standard deviation should have the same unit as the raw data you collected. For example, SD = +/- 0.5 cm.

What is standard error?

When you are conducting research, you often only collect data of a small sample of the whole population. Because of this, you are likely to end up with slightly different sets of values with slightly different means each time.

If you take enough samples from a population, the means will be arranged into a distribution around the true population mean. The standard deviation of this distribution, i.e. the standard deviation of sample means, is called the standard error.

The standard error tells you how accurate the mean of any given sample from that population is likely to be compared to the true population mean. When the standard error increases, i.e. the means are more spread out, it becomes more likely that any given mean is an inaccurate representation of the true population mean. In this course, we use eroor bars that show data within 95% confidence (+/- 2 SEM). See the video below for more information.

**Google sheets only allows Standard Error bars in a bar graph.

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