The introduction of a data summary is the place where the **writer explains** what the reader will learn and why they should read further.

How to write an introduction for a data summary? The author should first explain what data is and how it can be organized. Then, he or she should explain the different types of data summaries that can be written.

They can be organized by type (i.e. numerical, graphical, tabular), by topic (i.e. environment, economy, society), or some combination of the two.

The author should also explain how readers will *learn something new* or be inspired by reading their piece. This creates motivation for the reader to continue reading and appreciate the piece.

## Types of data summaries

All data does not need to be summarized, and in fact, most data does not need to be summarized. Summarizing data takes time and effort, so it is important to know when to summarize data and when not to.

There are several types of data summaries, each of which serves a different purpose. Some types of data summaries can be used in conjunction with each other, while others cannot.

The first type of summary is the verbal summary. This is just what it says: saying what the information in the data is. This can be done by just saying what is in the data or by listing some of the information in the data.

The *second type* of summary is the tabular summary. This lists all of the information in the data in a *table format*. These can be *created using software* or by hand drawing them.

## Visual data summaries

As we mentioned earlier, today’s world is information-rich, and the volume of data is growing at an exponential rate.

Information can be in many forms, such as verbal, numerical, graphical, or textual. Verbal information is spoken or uttered data, numerical information is data that is quantified or numbers, graphical information is images or pictures, and textual information is prose or written words.

All of these types of information can be summarized and integrated into a single piece of data that can be easily understood by anyone who sees it. The summaries can take any form depending on what type of data it summarizes.

There are *many different types* of visual data summaries that can be created to *help people understand complex datasets*. Some of these include: chart types (bar chart, circle graph), pie charts, dot plots (or bullet graphs), andsanational average line graphs.

## Tabular data summaries

A table, also called a dataset, is a *structured collection* of data. Tables are used in publications and documents such as books or news articles to display information.

They can be used in almost any *subject area*, especially when data is complex or needs to be organized into categories.

Tables can be organized by rows or columns, or sometimes both. They can also be organized by value, category, or magnitude. Depending on the table layout, different types of information may be conveyed.

There are *several things* that you should check when looking at a table to see if it is accurate. First, you should check the **sources listed** at the bottom of the table. Then, you should look at the numbers in the table and do some quick math to see if they add up.

## Nominal scale data summaries

The nominal scale is the simplest scale to use for data summaries. On this scale, data points are assigned a value based on their position relative to other points.

For example, a data point could be labeled “strongly disagree,” and all other data points would be labeled similarly. There would be no sense of order between these points; they would all be considered equal.

When creating a nominal scale summary, there are **two main things** that need to be done. The first is to determine the labels that will be used and in what order. The second is to count how many labels there are and how **many data points fall** into each label.

This can be very simple if there is only one level of intensity for all labels or if there is only one label given to all data points. More *complex datasets may require* more sorting and counting of labels to create an accurate summary.

## Ordinal scale data summaries

Ordinal scale data refers to data that ranks things in order or hierarchy. For example, grades rank students on a scale of A to F.

Ordinal scales can be numerical, graphical, or tabular summaries. A *numerical ordinal scale summary would list* all students’ grades as numbers, from highest to lowest grade. A *graphical ordinal scale summary would draw* a bar or pie chart with the same ordering. A **tabular ordinal scale summary would list** all students’ names and the grades they received.

All of these summaries would be the same, with the exception of the tabular version listing the names. All of these ordinal scale data summaries are useful because they show the relative ranking of things and how many things fall into each category.

For example, on a grade scale of A to F, an A is the highest and an F is the lowest. There are more As than Bs, more Bs than Cs, more Cs than Ds, and more Ds than Fs.

## Mean and median

Mean is the average of a set of data. Median is the middle value of a set of data, with an even number of values. Mean and median are very different numbers, and can be very different representations of data.

Mean is *often used* as an average due to its simplicity. It is calculated by adding all the values in the set and dividing by how many values there are.

For example, let’s say we have a set of numbers: 1, 2, 3, 4, 5. The mean is 2.8 (1+2+3+4+5=10; 10/5=2.8). The median is 3 (there are an even number of numbers less than or equal to 3).

There are **many cases** in which mean is not representative of data. One such case is income; someone can earn $*100k per year* but be in the middle (median) for that demographic.

## Range

A range list is a summary of the ranges of values a *data set contains*. Ranges can be any value, such as numbers, gender identities, or races.

Range lists are very useful in public settings. For instance, if a business wants to ensure they have an equal number of male and female customers, they can quickly and easily check their customer list by the number of ranges of genders they have.

They would simply have to divide their customer base by male and female and then count the numbers of each. This would be quick and easy thanks to the **range lists provided** by the business.

Range lists can be created by anyone with *basic numerate skills*. People who are unskilled in *numerate skills may need* some help determining what races or genders exist, but that is relatively easy to fix.

## Standard deviation

A metric that is often discussed when talking about median salary is the median salary plus or minus the standard deviation. This is because **many people use** this data point to determine if a job is a good salary or not.

For example, if the median salary for a position is $50,000 and the standard deviation is $10,000 then any job paying $40,000-$60,000 would be considered a **decent pay rate**.

This is because you would be making the median salary plus the standard deviation which would put you in the middle of the pack. You would not be paid below average but not above either.

However, this can be very misleading and *unfortunately puts people* who are paid below average at a disadvantage. This is because people who are actually paid below average will think they are being paid well when they are actually receiving a **low pay rate**.