Introduction to Statistics With Relevant Examples

Statistics refers to concepts, rules, and procedures that help us interpret data and make informed decisions regarding issues affecting our lives and humanity in general. Data is basically facts or observations that result from an investigation. Statistics is a wide field of study that has relevance across most areas, including the economy, academic, and industrial research. There are two main branches of statistics — descriptive and inferential statistics.

Descriptive Statistics

Descriptive statistics provide simple summaries of data. They represent complex data in a manageable form and do not generalize data. A good example is the average height of men in a country. Measures of descriptive statistics include the mean, variance, kurtosis, and skewness.

Inferential Statistics

This entails using the statistical sample data to draw valid conclusions concerning the entire population. Under inferential statistics, we have probability distributions, hypothesis testing, correlation/regression analysis, and probability distributions.

Population vs. Sample

A population refers to the summation of all the elements of interest to the researcher. For example, these could be the number of people in a country, the number of animals in a zoo, or the total number of cars in a given county.

A sample is just a set of elements that represent the population as a whole. It is s very difficult to collect data from every element in the population. This calls for the use of a sample comprising a small number of representative elements. By analyzing sample data, we can make conclusions about the entire population. Thus, sampling makes the analysis of a large population manageable and helps researchers save time.

Types of Measurement Scales in Statistics

We use measurement scales to categorize variables. There are four main categories:

1. Nominal Scales

Nominal scales are used to label variables but have no inherent numerical significance. A good example would be gender representation, e.g., 1 to represent ‘male’ and 2 to represent ‘female.’

2. Ordinal Scales

Ordinal scales represent ordered categories where each category has an ordered relationship to all the other categories. Note that it is the order of important categories but not the differences between them, which cannot be quantified. A good example is a rating scale starting from 1 to 3, where 1 represents ok, 2 for good, and 3 for excellent.

3. Interval Scale

With interval scales, we know both the order and the exact differences between the values. A good example of this type of scale is time because we can establish the exact increments or decrements. An even clearer example is temperature measurement in Celsius – the difference between, say, 60 and 80 degrees is a measurable 20 degrees.

4. Ratio Scales

Ratio scales are complete because they tell us about the order, the exact differences between values, and have a true zero. Thus, we can calculate ratios. Height and weight are good examples of ratio variables. Consequently, ratio scales pave the way for measures of central tendency such as the mode and the mean and measures of dispersion, e.g., standard deviation.