Central Tendency: Dot Plots, Histograms & Box Plots

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  • 0:04 What Is Central Tendency?
  • 0:48 Central Tendency Dot Plots
  • 2:16 Central Tendency Histograms
  • 3:07 Central Tendency Box Plots
  • 4:53 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

To quickly visualize and categorize groups of data, we can use graphical representations like dot plots, histograms, and box plots. In this lesson, you will learn how to create and interpret these important graphs.

What Is Central Tendency?

Central tendency is defined as the typical value of a set of data. There are three main ways that we measure central tendency: mean, median, and mode.

The mean is the average of all the data. To find the mean, add up all the values and then divide by the number of values. The median is the value that is exactly in the middle of a list of the data, after it's been arranged in numerical order. The mode is the most commonly occurring number in the data set. Although these measures of central tendency are very useful, sometimes it's not enough just to know the mean, median, or mode. Sometimes, you need to represent data graphically in order to see any underlying patterns.

Central Tendency Dot Plots

One of the simplest ways to represent a set of data graphically is a dot plot. Dot plots are graphs that show the number of times that each data point occurs by the placement of dots. For example, if a teacher wanted to know how many books his students read last month, he could collect the data, organize it into a table like the one on your screen below, and then make a dot plot like the one shown on screen below that. In this dot plot, each dot represents one student.

Data gathered by a teacher on the number of books read in a one month by students
data table

This dot plot represents how many books were read by students in a class during one month. Each dot represents one student.
dot plot

Dot plots are really good for identifying the mode of a data set, which in this case are seven and nine. This means that more students read seven or nine books during the last month than any other number of books.

The median can be found by locating the point that is exactly in the middle. Here, the median is 4.5 books because there are 50 dots in total, and dot 25 is at four books and dot 26 is at 5 books.

To find the mean, you need to calculate a weighted average. Multiply each number of books by the number of students above it. Then add all these and divide by the total number of students (50) to find the mean.

Mean = ((0 x 3) + (1 x 3) + (2 x 7) + (3 x 6) + (4 x 6) + (5 x 3) + (6 x 4) + (7 x 8) + (8 x 2) + (9 x 8)) / 50 = 4.8 books

Central Tendency Histograms

A histogram shows the frequency of how often a certain value occurs using a bar graph. Histograms are used to visualize the distribution of data.

To make a histogram:

  1. Decide how many groups you want to have, and separate the data into groups.
  2. On the x-axis, label the value of each group, and on the y-axis, label the number of data points in each group (the frequency).
  3. Draw a bar that is the height of the frequency for each group.

A histogram of our example data is shown on your screen below. This histogram has a group size of 1 book, so there are 10 different groups.

histogram example

From a histogram, you can quickly see how the data is distributed, and this helps you decide how to analyze the data further. In this histogram, there is not a clear pattern in the data, but in many cases, there will be.

Central Tendency Box Plots

Box plots, also known as box-and-whisker plots, only show a summary of the data, including the median and minimum and maximum values. They are used to quickly compare different sets of data with each other.

To make a box plot:

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