How do we categorize and make sense of data? Statistics 101 How do we categorize and make sense of data?

Categories of data: Qualitative data is not numerical and is usually subjective. Quantitative data is numerical and lends itself to statistical analysis. http://ibscrewed4maths.blogspot.com/2011/03/types-of-data.html 1.75 mL

One of the first steps in data analysis is to create graphical displays of the data. Visual displays can make it easy to see patterns and can clarify how two variables affect each other. AP Biology Quantitative Skills Manual

For parametric data (a normal distribution), the appropriate descriptive statistics include : sample size(n) the mean (average) range variance / standard deviation standard error AP Biology Quantitative Skills Manual

The mean (x)of the sample is the average The mean (x)of the sample is the average. The mean summarizes the entire sample and might provide an estimate of the entire population’s true mean. AP Biology Quantitative Skills Manual

Measures of Dispersion about the mean Range - the simplest of our methods for measuring dispersion is range.  Range is the difference between the largest value and the smallest value in the data set.  Range = Highest value – Lowest value 

Variance  (s2) and standard deviation (s) measure how far a data set is spread out. A variance of zero indicates that all the values in a data set are identical. AP Biology Quantitative Skills Manual Distance from the mean Variance

The standard deviation is the square root of the variance The standard deviation is the square root of the variance. The standard deviation is expressed in the same units as the original data set, which makes it generally more useful than the variance. Standard deviation is useful or important because it illustrates how much dispersion or variation exists from the mean, average or expected value. AP Biology Quantitative Skills Manual

Let’s Try It! Using the following test score distribution, 92% 66% 99% 75% 69% 51% 89% 75% 54% 45% 69% Determine: n (sample size) Mean Range Standard Deviation

Steps in calculating Standard Deviation Step 1-Find the mean of the data (in other words, take an average of all your data points) Step 2-Subtract the mean from each data point Step 3- Square of the values you got in step 2 Step 4-Subtract 1 from the number of data points you used in step 1. Step 5- Divide your answer in step 3 by your answer in step 4. Step 6 -Find the square root of the answer you got in step 5.

A little more than two-thirds of the data points will fall between +1 standard deviation and −1 standard deviation from the sample mean. More than 95% of the data falls between ±2 standard deviations from the sample mean. AP Biology Quantitative Skills Manual

68–95–99.7 Rule http://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule AP Biology Quantitative Skills Manual In a normal distribution, 68.27% of all values lie within one standard deviation of the mean. 95.45% of the values lie within two standard deviations of the mean. 99.73% of the values lie within three standard deviations of the mean.

A small standard deviation indicates that the data tend to be very close to the mean. A large standard deviation indicates that the data are very spread out away from the mean. AP Biology Quantitative Skills Manual

Sample standard error (SE) is a statistic used to make an inference about how well the sample mean matches up to the true population mean. AP Biology Quantitative Skills Manual

Standard error should be represented by including error bars on graphs when appropriate. Error bars are used on graphs to indicate the uncertainty of a reported measurement.  AP Biology Quantitative Skills Manual

Error Bars