Descriptive and inferential statistics each give different insights into the nature of the data gathered. One alone cannot give the whole picture. Together, they provide a powerful tool for both description and prediction.

## Categorizing Statistics

The study of statistics can be categorized into two main branches. These branches are descriptive statistics and inferential statistics.To collect data for any statistical study, a population must first be defined.

Population‘ indicates a group that has been designated for gathering data from. The data is information collected from the population. A population is not necessarily referring to people. A population could be a group of people, measurements of rainfall in a particular area or a batch of batteries.

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## Descriptive Statistics

Descriptive statistics give information that describes the data in some manner. For example, suppose a pet shop sells cats, dogs, birds and fish.

If 100 pets are sold, and 40 out of the 100 were dogs, then one description of the data on the pets sold would be that 40% were dogs.This same pet shop may conduct a study on the number of fish sold each day for one month and determine that an average of 10 fish were sold each day. The average is an example of descriptive statistics.Some other measurements in descriptive statistics answer questions such as ‘How widely dispersed is this data?’, ‘Are there a lot of different values?’ or ‘Are many of the values the same?’, ‘What value is in the middle of this data?’, ‘Where does a particular data value stand with respect with the other values in the data set?’A graphical representation of data is another method of descriptive statistics.

Examples of this visual representation are histograms, bar graphs and pie graphs, to name a few. Using these methods, the data is described by compiling it into a graph, table or other visual representation.This provides a quick method to make comparisons between different data sets and to spot the smallest and largest values and trends or changes over a period of time. If the pet shop owner wanted to know what type of pet was purchased most in the summer, a graph might be a good medium to compare the number of each type of pet sold and the months of the year.

## Inferential Statistics

Now, suppose you need to collect data on a very large population. For example, suppose you want to know the average height of all the men in a city with a population of so many million residents. It isn’t very practical to try and get the height of each man.This is where inferential statistics comes into play.

Inferential statistics makes inferences about populations using data drawn from the population. Instead of using the entire population to gather the data, the statistician will collect a sample or samples from the millions of residents and make inferences about the entire population using the sample.The sample is a set of data taken from the population to represent the population. Probability distributions, hypothesis testing, correlation testing and regression analysis all fall under the category of inferential statistics.In inferential statistics, the answers are never 100% accurate because the calculations use a sample taken from the population. This sample doesn’t include every measurement from the population, and the methods use probability to fill in missing gaps. To account for this, another aspect of inferential statistics covers ways to lessen the margin of error and ways to control how much error you introduce into your calculations.

This is known as statistical estimation.Combined with probability, inferential statistics becomes a very powerful tool for making inferences and predictions about large populations.In the city with millions of residents, inferential statistics will provide the answer to a question such as ‘What is the probability that a man from this city is less than 6 feet tall?’If a drug company claims that their new drug cures diabetes, you could use inferential statistics to answer the question ‘How accurate is the claim that this new drug cures diabetes?’ Another study with the same drug may point to an increase in heart attacks in patients that take this new drug. Inferential statistics provides the tools to test that claim as well.

A college could use inferential statistics to answer questions such as ‘How many bachelor’s degrees do we anticipate will be awarded in 2015?’ If a college is planning courses to offer for a future term, inferential statistics might be used to anticipate enrollment and to decide how many English 101 classes should be offered based on those numbers.

## Lesson Summary

In summary, statistics is categorized into two branches – descriptive and inferential. Descriptive statistics uses the data to provide descriptions of the population, either through numerical calculations or graphs or tables. Inferential statistics makes inferences and predictions about a population based on a sample of data taken from the population in question.

## Learning Outcomes

Upon completing this lesson, you will be able to:

• Define data, population and sample
• Differentiate between descriptive and inferential statistics