Once you have data, there are various things you may want to analyze about it. One vital reason for wanting to use numerical data is that it is easier to analyze, and there is more you can do with it.

For example, Figure 3.2 Sample spreadsheet of performance appraisal data shows performance appraisal scores for the period 2003 to 2006 using a scoring system for employees scoring them from 1 to 10.

Imagine you want to analyze the 2006 performance appraisal data from Figure 3.2 Sample spreadsheet of performance appraisal data. You could:

Take a look at the 2006 scores from Figure 3.2 Sample spreadsheet of performance appraisal data. If we look at the column of data, then we see that we have a range of data from 2 (the lowest in the list) to 10 (the highest). If we order it from lowest to highest then it is:

2, 3, 5, 5, 6, 6, 6, 7, 8, 10

We see two major things about the data already:

There is more we could ask: what kind of data is it (compared, say, to an appraisal system where employees are ranked only on a system of “Below Average,” “Acceptable” and “Above Average”)?

There are therefore multiple aspects or characteristics of numerical data that we need to understand – these characteristics and our understanding of them have a fundamental impact on our ability to analyze them as well as our understanding of the analysis.

As we have seen, each variable is measured across multiple observations, such as a survey question measured across many employees. Because the variable is measured across many observations, which can differ in their response to the variable, there are a range of measured responses to each variable. This brings up three very important characteristics of variables:

Let us explore these three characteristics of data more thoroughly.

As mentioned earlier, when looking at a variable, centrality is the most representative data point, the score most of the sample tends towards. The average or mean is an example of a specific centrality statistic, although as explained in Chapter 7 you cannot use the average for all data. The type of centrality measure depends on the type of variable. I discuss different types of centrality statistics in Chapter 7.

A quick note: measures of centrality are by far the most used and important measures of practical statistics, especially in business. Market research, for instance, is principally concerned with average levels of variables such as spending or customer attitudes, especially between geographical or demographic segments. Financial research might look at average returns in various investment portfolios. HR research wants to know about variables such as average time to fill a vacancy.

However, measures of centrality are only a start to really understanding data. The spread of the data is also crucial.

Remember that different observations vary in their scores on a given variable. If you measure age across a sample of multiple people, their ages will differ. Spread expresses this crucial characteristic of a variable, namely that there is a range of data on either side of the middle. The larger the spread of the data away from the middle, the less that the central score represents the whole dataset and the more that every observation is different from the others.

As an illustration, take a look at two different sets of data in Figure 3.4 Examples of different spreads in data below.

In Figure 3.4 Examples of different spreads in data we see that:

Data that has a natural order from low to high (interval, ratio, and even ordinal data) inevitably has a range: that is, such variables range from some low to some high. The ages of workers in the company, for instance, might range from an absolute low of 17 to a high of 67. Categorical data also has spread, but this is harder to think about on a low to high basis, for such data you are thinking about relative distribution of observations between categories.

Minima and maxima of sets of data can be useful to know as an absolute measure of spread, because they tell you the absolute lowest score to the absolute highest. They do not, however, tell you anything about where in the range the center of the data lies, or where the majority of the data lies. The employee age endpoints of 17 and 67 might be extreme outliers (there might be very few employees with age as low as 17 or as high as 67). Statistical measures of spread that capture the majority of observations without also taking in the extreme outliers at the far ranges are better measures. There are several such spread-base statistical measures, such as the standard deviation and inter-quartile range, as discussed in Chapter 7.

Spread might be the most important thing in statistics. I encourage you to read the spread sections later in the book carefully until you understand them. Later, we will see why this concept is so critical.

Business statistics succeeds or fails depending on whether you pick the right data (observations and variables) to study, and whether you measure them in a valid and reliable way. Chapter 4 discusses these issues in more depth, as well as the broad challenges around actually gathering, capturing and cleaning datasets.