# What does a peak in the distribution of your data mean?

May 25, 2017

See below.

#### Explanation:

A peak in the data shows that you have a large number of respondents or a high rate at a certain point along your x axis. You can have multiple peaks in your data and they can be gradual or sharp. Data that is more peaked is data that has a sharper peak compared to data with a more gradual slope. Gradual peaks indicate that your data rose steadily whereas a sharp peak indicates that your values increased rapidly.

(Kurtosis is the term used to describe the sharpness of the peak in a frequency distribution curve.)

In the graph below, the first series of data (blue) has a sharp peak at 8 on the x axis whereas the second series of data (orange) has a more gradual peak at 6 on the x axis. The first series is more peaked than the second.

The exact interpretation of a peak will depend on what your data is and what it is being compared to. Are we looking at a graph showing frequency of trips to the emergency room on college campuses or are we looking at a graph showing monthly retail sales? Our interpretation of the peaks will depend on the context and the information we have available.

For example, if the graph below shows the number of alcohol-related emergency room (ER) visits by week for college students, with the first series (blue) representing first year students and the second series (orange) representing second year students, the second year students show a more peaked distribution.

The number of alcohol-related ER visits for first year college students peaks around the second/third week and gradually declines. Whereas the second year college students have relatively fewer alcohol-related ER visits until the 8th week of school when there is a sharp peak in the number of visits.