Course: Research Methods
The average, a measure of central tendency, is the sum of all values divided by the total number of values.
Understanding Averages
In social research, the term average is often thrown around. But what does it really mean? An average, in the simplest terms, is a single number representing a set of numbers. It helps us summarize a bunch of numbers with one single value that represents the ‘middle’ or the ‘central tendency’ of the data. It gives us an idea of where most values in the data set lie.
There are different types of averages, but the most common one is the mean, which we often just call the ‘average.’
The Mean: A Closer Look
The mean is calculated by adding up all the numbers in a data set and then dividing by the total number of values. For example, if we have the numbers 2, 4, and 6, the mean would be (2+4+6) / 3 = 4. The mean gives us a useful measure for many sets of data.
Averages in Action: Diverse Fields, Same Principle
The concept of averages and mean is used across various fields, including criminal justice, social work, and political science. Let’s explore how.
Criminal Justice
In criminal justice, averages could be used to find the average number of years that convicts serve in prison for a particular crime. Let’s say we have data for five individuals: 3 years, 5 years, 7 years, 5 years, and 6 years. The average would be calculated as (3+5+7+5+6) / 5 = 5.2 years.
Social Work
In social work, an average might be used to understand the average number of caseloads a social worker has per week. If a social worker sees 5, 7, 8, 6, and 7 cases in five consecutive weeks, the average weekly caseload would be (5+7+8+6+7) / 5 = 6.6 cases.
Political Science
In political science, the average can be used to measure the average public opinion on a certain policy issue. Suppose a rating out of 10 is gathered from 100 individuals. The average rating would provide a sense of the overall public sentiment.
Always Remember: Context is Key
While averages are very useful, they should always be used with care. They can sometimes be skewed by very high or very low values, which could make the average less representative of the majority of values. It’s crucial to consider the whole data set and other statistics like the median and mode.
The mean, or average, is an incredibly helpful tool for understanding data. But it doesn’t come without its assumptions and limitations. When we are dealing with extreme scores, or outliers, the mean might not always represent our data accurately. And there are several assumptions we make when using the mean as a measure of central tendency.
Extreme Scores and Their Effect on Mean
Extreme scores, or outliers, are values that significantly differ from other observations. They can heavily impact the mean. For instance, let’s consider the incomes of five individuals: $30,000, $35,000, $40,000, $45,000, and $1,000,000. The mean income would be $230,000, which is heavily skewed due to the last value.
This example shows that the mean can sometimes give a misleading picture. Most people in this data set earn around $37,500, not $230,000. In such cases, other measures of central tendency, like the median or mode, might be more helpful.
Assumptions of the Mean
When we use the mean, we make several assumptions. Here are two important ones:
- Interval or ratio data: To calculate the mean, we assume that the data are either interval or ratio data. These types of data are numerical and allow for a wide range of statistical analyses. They give us meaningful averages. For example, we can average temperatures or weights, but it doesn’t make sense to average categories like ‘apples’ and ‘oranges’ or ‘agree’ and ‘disagree.’
- Symmetrical distribution: We often assume that the data are symmetrically distributed when we calculate the mean. This means that the values are evenly distributed on both sides of the mean. However, this is often not the case, especially with outliers in the data.
The Mean in the Real World: A Critical Tool, but Use with Care
The mean is a powerful tool in fields like criminal justice, social work, and political science. It allows us to understand the central tendency of years served for crimes, average caseloads, or public opinion. But it’s essential to remember that outliers can skew the mean, and not all data meet the assumptions necessary to use the mean effectively.
While the mean can be incredibly useful, it doesn’t tell the whole story. It’s always a good idea to look at your data from different angles and use other measures of central tendency, like the median or mode, especially when dealing with outliers. This way, we ensure that we have a complete and accurate understanding of our data.