This document discusses various methods for graphically displaying data in statistics, including time series graphs, bar charts, histograms, circle graphs, dot plots, stem plots, ogives, and indicators of misleading graphs. It provides examples and descriptions of how to properly interpret and construct each type of graph. Key points include showing change over time with time series graphs, comparing categories with bar charts, displaying continuous or binned data with histograms, showing percentages with circle graphs, listing all values with dot and stem plots, and calculating cumulative frequencies with ogives. Misleading graphs are identified as those that distort scale, lack labels, omit data, or have uneven bins.

1. Graphical Displays of Data
AP Stats Unit 1
There are several different methods used to display data in Statistics. Time
Series Graphs, ar Graphs, Histograms,
Each have their most common characteristics. However, not every graph you
see follows those characteristics without fail. The important thing is that you
know how to interpret the data presented and to look out for misleading
graphs.

2. Time Series Graph
Use a time series graph to do what it sounds like it will do - show the change in
a variable over time.
Time on horizontal axis - Variable on vertical axis

3. This is a great example of a time series graph. It also is misleading if you
compare values by looking at the distance between the lines. In 2100, it looks
as if the temperature on the red line is 4 times higher than the black line. In
reality, it’s 4 degrees difference since the vertical axis doesn’t start at 0. Pay
attention to labels!
Title: Surface Air Temperature | Source: Earth Exploration Toolbook | Public Domain

4. Bar Charts Segmented Bar
Charts
Use bar charts when comparing items between different groups. Segmented
bar charts may be used to show two or more variables
Bars have gaps between and positioned over a label that represents a
categorical variable.
Height of the bars indicates the frequency of the data and are used to make
comparisons.
All bins (bars) should have the same width.

5. Using this segmented bar chart, you can compare not only total values but also
values of referrals for each of four people in the months of March, April, and
May.

6. Histogram
Use histograms when you have continuous data such as height or ranges of
values such as 1-5, 6-10, etc.
Histograms usually leave no gaps between bins/intervals.
Used for LARGE sets of data

7. This histogram is labeled
properly if we believe that the
number of SNPs above 15 for
the interval 0.00 and 0.01 is
represented correctly by the
height of the bin. The only way
to know for certain is by
looking at the original data.

8. Circle Graphs
AKA Pie Charts
Use circle graphs to show the
percentage of categorical variables in
a data set.
Percentages should total 100%.
Although the actual percentages are
not labeled on this circle graph, we
can make good approximations and
comparisons based on the
characteristics of circle graphs.

9. Dot Plots
Use a dot plot to display EVERY value of a variable.
Used for small data sets
3/10 or 30% of these families have 1 pet.
*
* * *
* * *
* * *
0
1 2 3 4 5 6 7 8

10. Stem Plot AKA Stem-and-Leaf Plot
Use a stem plot to display all the values of a discrete data set.
The stem and leaves are separated by a vertical line. The numbers are listed
from the stems out; i.e., 13 | 1 1 4 6 8 represents data values 131, 131, 134,
136, 138
Stems are listed vertically from lowest to highest.

11. In this back-to-back stem and leaf
plot you can compare battery life of
Brand A and Brand B.
Brand A had the lowest recorded
battery life of 5 hrs compared to
Brand Bs low of 7 hrs.
You can’t make inferences that
can’t be supported such as Brand B
is better than Brand A.
Image Copyright 2013 by Passy’s World of Mathematics

12. Ogive
Use an ogive to graph
cumulative frequencies for a
set of data.
Used to calculate frequency
of data above or below
specific values
In this ogive, plotting cumulative frequencies of
psychology test scores, by carefully extracting values you
can make statements like:
Approximately 460/650 or 71% scored below 95.
Approximately 110/650 (200-90) or 17% scored between
65 and 75.
Your ability to estimate values between labels is
important in how closely your estimation represents the
actual data.
Photo Source: Online Statistics Education: A Multimedia Course of Study
(http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University.

13. Misleading Graph Indicators
Vertical scale is too big or small, skips numbers, doesn’t start at zero
Not labeled properly.
Data is left out.
Bins (bars) are not the same width.