application of 

statistical methods to medical and biological 

problems

to make an 

inference about a population, based on 

information contained in a sample

***subject to error and/or bias

totality of subjects under study



***sometimes referred to as the parent 

distribution***

subset of the population actually 

studied



***sometimes referred to as the sample 

distribution***

*Collect information/data from

*Can be people, animals, plants, or any object of 

interest

*is any characteristic of an individual. A variable varies among individuals

***Example: age, height, blood pressure, ethnicity, leaf length, first language***

tells us what values the variable takes and 

how often it takes these values

Something that takes numerical values



***Example: How tall you are, your age, your blood pressure, the number of credit cards you own***

Something that falls into one of several categories. What can be counted is the count or proportion of individuals in each category



***Example: Your blood type (A, B, AB, O), your hair color, your ethnicity, whether you paid income tax last tax year or not***

Because the variable is categorical, the data in the graph can be ordered any way we want (alphabetical, by increasing value, by year, by personal preference, etc.)

***Example: Bar graphs and Pie charts***

*Each category is represented by a bar

*The bar’s height shows the count (or sometimes the percentage) for that particular category

*The slices must represent the parts of one whole

*The size of a slice depends on what percent of the whole this category represents

*Histograms and stemplots

*Line graphs: time plots

*These are summary graphs for a single variable

*They are very useful to 

understand the pattern of variability in the data

*Use when there is a meaningful sequence, like time

*The line connecting the points helps emphasize any change over time

*Range of values that a variable can take is divided into equal size intervals

*Shows the number of individual data points that fall in each interval

How to make a stemplot:

1) Separate each observation into a stem, consisting of all but the final (rightmost) digit, and a leaf, which is that remaining final digit

2) Write the stems in a vertical column with the smallest value at the top, and draw a vertical line 

3) Write each leaf in the row to the right of its stem, in increasing order out from the stem

*Stemplots are quick and dirty histograms that can easily be done by hand

*However, they are rarely found in scientific or laymen 

publications

*Symmetric

*Skewed Right

*Skewed Left

*An important kind of deviation is an outlier. Outliers are observations that lie outside the overall pattern of a distribution

*Always look for outliers and try to explain them

*In a time plot, time always goes on the horizontal, x axis

*We describe time series by looking for an overall pattern and for striking deviations from that pattern

*In a time series there are trends and seasonal variation

A rise or fall that 

persists over time, despite 

small irregularities

*Average

*Q2

The value in the sample that has 75% of the data at or 

below it

*Outliers are troublesome data points, and it is important to be able to identify them

*One way to raise the flag for a suspected outlier is to compare the distance from the suspicious data point to the nearest quartile (Q1 or Q3)

*Then compare this distance to the interquartile range (IQR)(distance between Q1 and Q3)

*“1.5 * IQR rule for outliers

*"s" is used to describe the variation around the mean

*Like the mean, it is not resistant to skew or outliers

*s measures spread about the mean and should be used only when the mean is the measure of center.



*s = 0 only when all observations have the same value and there is no spread. Otherwise, s > 0.



*s is not resistant to outliers. 

*s has the same units of measurement as the original observations.

*Variables can be recorded in different units of measurement

*Linear transformations do not change the basic shape of a distribution (skew, symmetry, multimodal)

*But they do change the measures of center and spread

one axis is used to represent each of the variables,

and the data are plotted as points on the graph

*measures or records an outcome of a study

*is the y-axis

*explains changes in the response variable

*is the x-axis

X and Y vary independently. Knowing X tells you nothing 

about Y

*average the y values separately for each x value

 *When a data set does not have many y values for a given x, software smoothers form an overall pattern by looking at the y values for points in the neighborhood of each x value

*Smoothers are resistant to outliers