Describing Distributions
When making graphs of quantitative data, it is important to be able to tell what the graph is “saying”. In general, you do this by looking for an overall pattern and also for striking deviations from that pattern.
Aspects of the overall pattern are as follows: 1. Shape 2. Center 3. Spread 4. Unusual Characteristics
1. Shape Shape: Distributions come in an endless variety of shapes; however, certain common patterns can occur. A. Symmetrical B. Skewed C. Bimodal
Symmetrical refers to data in which both sides are (more or less) the same when the graph is folded vertically down the middle. Some special cases of symmetrical distributions are uniform distributions, where all values (or groups of values) occur with (approximately) equal frequency and bell- shaped distributions – one of which, the normal distribution, we will discuss in great detail later.
Bell Shaped
Uniform
Skewed a skewed distribution is asymmetrical. The distribution has one “tail” that stretches out much further than the other side of the distribution, indicating one or a few values that are noticeably larger/smaller than the majority of the values. A distribution can be skewed either left or right, which indicates the direction of the tail.
Skewed Left
Skewed Right
Bimodal (or multimodal) – refers to data which has two (or more) clear, separate “high points”, or high frequencies.
Bimodal
2. Center We will discuss center more formally later on, but the center generally is the point that one would say is your outcome, on average. Generally, the value that splits the data in half (the median) is used to describe the center of a graphical display.
3. Spread This will also be discussed more formally later on, but the spread is usually given by reporting the smallest and largest data values, disregarding (but commenting on later) outliers, which are unusually high or low values (we will learn one method to calculate whether a value is an outlier later on).
4. Unusual Characteristics Any gaps, outliers, clusters (noticeable data groupings) or other unusual characteristics should be reported.
Describing Distribution When describing your distribution, always remember to CUSS your graph! C enter U nusual Characteristics S hape S pread