Data presentation in statistics

Data presentation in statistics is done using tables, charts, diagrams, or graphs and is part of the data analysis and reporting phase of the data analysis life cycle. Visual data presentation helps data analysists identify and understand relationships between and within data sets to inform science-based decision making. This post constitutes Lesson 2 of the Basic Statistics Mini-Course.

You may be also interested in Measures of central tendency.

Key concepts covered in this post: frequency distributions and histograms, graphical representations of data, comparing graphs, stem and leaf plots.

Frequency distributions and histograms

Collected data can be organized in a frequency table and displayed in a histogram to make it easy to notice important features or patterns in the data.

For example, we’re trying to know how far a turtle can travel in half an hour. The distances traveled by 50 turtles in half an hour are recorded rounded to the nearest centimeter.

2	82	64	73	89	38	55	99	63	25
48	106	33	27	54	61	114	60	58	51
21	51	41	93	53	11	15	39	86	66
121	49	75	46	29	71	26	19	73	53
35	23	97	84	56	75	60	59	32	46

Often, collected data are grouped into suitable intervals before displaying them in a frequency table and then in a histogram.

When grouping data 1) choose intervals of the same length, 2) try to keep the number of intervals between 5 and 20 (to help maintain clarity), and 3) do not leave gaps between the bars of the histogram (Google Spreadsheets may not allow you to completely remove the gaps between the bars).

Suppose we find that the smallest distance traveled by a turtle in half an hour was 2 cm and the largest was 121 cm, a spread covering 120 numbers. For the purpose of this illustration, 10 intervals of 12 can be used to organize the data in a frequency table.

Distances (cm)	Frequency
2-14	2
14-26	5
26-38	6
38-50	7
50-62	12
62-74	6
74-86	4
86-98	4
98-110	2
110-122	2

Use the middle number of an interval to label the horizontal axis. In this example, the most common distance traveled by a turtle in half an hour was 56 cm.

Graphical representations of data

Choose the type of graph that best explains the results.

Pie charts (circle graphs) show how something is divided (a breakdown of the parts of the whole), e.g., how the government spends $1.00 of tax revenue;

Broken line graphs visualize how something changes over time, e.g., the changing value of the dollar over time;

Bar charts compare things that are alike, e.g., the heights of the mountains of North America;

Pictographs (pictos) show information using images (present the information visually), e.g., a visualization of Canada’s exports.

Comparing graphs

Businesses can plot their expenses and revenues on the same axis (Y axis) over the years (x axis) to help them analyze their financial position. The same scale must be used for both sets of data. Where the revenue line and the expense line cross is the break-even point (when the amount earned is equal to the amount spent).

Stem and leaf plots

A stem and leaf plot looks like a histogram on its side. But unlike histograms, stem and leaf plots retain the original data to at least two significant digits and order the data to facilitate order-based inference and non-parametric statistics.

The first part of a number is the stem and the second part is the leaf, e.g., 48.6 could be written with 48 as the stem and 6 as the leaf.

Stem and leaf displays present quantitative data in a graphical format to assist in visualizing the shape of a distribution.

The stem is used to group the scores and each leaf shows the individual scores within each group. You can see how the results cluster (leaves around stems).

See some examples at https://www.mathsisfun.com/data/stem-leaf-plots.html

Next post: Part 3: Measures of central tendency

Key concepts: Mean, median, mode, the effect of distribution on measures of central tendency.

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