What is Statistics?

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Overview

You are probably asking yourself the question, “When and where will I use statistics?” If you read any newspaper, watch television, or use the Internet, you will see statistical information. There are statistics about crime, sports, education, politics, and real estate. Typically, when you read a newspaper article or watch a television news program, you are given sample information. With this information, you may make a decision about the correctness of a statement, claim, or “fact.” Statistical methods can help you make the best educated guess.

Since you will undoubtedly be given statistical information at some point in your life, you need to know some techniques for analyzing the information thoughtfully. Think about buying a house or managing a budget. Think about your chosen profession. The fields of economics, business, psychology, education, biology, law, computer science, political science, and early childhood development require at least one course in statistics.

Included in this lesson are the basic ideas and words of probability and statistics.

Summarize, Represent, and Analyze Data

The science of statistics deals with the collection, analysis, interpretation, and presentation of data. We see and use data in our everyday lives.

Data may be numbers or words, and datum is a single value of data.

Take a look at the dot plot below. A class of 14 students answered the question, “On average, how many hours of sleep do you get per night?”

Instead of a cluster of numbers, the dot plot serves as a visual summary of the entire of set of data. Each dot represents a single datum. For example, the three dots above the 6 tick show that 3 students claimed they get 6 hours of sleep on average.

According to the data, what would most likely be the average amount of time spent sleeping per night? Between what values does your data set fall? What would be an unexpected value to add to your data set? These questions ask you to analyze and interpret your data. This is what you might do while studying statistics.

Two Types of Statistics

Organizing and summarizing data is called descriptive statistics. Two ways to summarize data are by graphing and by using numbers (like finding an average). Once you have a good understanding of descriptive statistics, you can use it to draw conclusions from good data. The formal methods to draw these conclusions are called inferential statistics. Statistical inference uses probability, the likelihood of an event occurring, to determine how confident we can be that our conclusions are correct.

Effective interpretation of data, called an inference, is based on good procedures for producing data and thoughtful examination of the data. In statistics, you will encounter what will seem to be too many mathematical formulas for interpreting data. The goal of statistics is not to perform numerous calculations using the formulas, but to gain an understanding of your data. The calculations can be done using a calculator or a computer, but the understanding must come from you. If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life.

Population and Sample

In statistics, we generally want to study a population. You can think of a population as a collection of persons, things, or objects under study. To study the population, we select a sample. A sample is a portion (or subset) of the larger population, and we study that portion to gain information about the population. Data are the result of sampling from a population.

Because it takes a lot of time and money to examine an entire population, sampling is a practical technique. If you wished to compute the overall grade point average at your school, it would make sense to select a sample of students who attend the school. The data collected from the sample would be the students’ grade point averages. In presidential elections, opinion poll samples of 1,000–2,000 people are taken. The opinion poll is supposed to represent the views of the people in the entire country. Manufacturers of canned carbonated drinks take samples to determine if a 16 ounce can contains 16 ounces of carbonated drink.

From the sample data, we can calculate a statistic. A statistic is a number that represents a property of the sample. For example, if we consider one math class to be a sample of the population of all math classes, then the average number of points earned by students in that one math class at the end of the term is an example of a statistic. The statistic is an estimate of a population parameter. A parameter is a numerical characteristic of the whole population that can be estimated by a statistic. Since we considered all math classes to be the population, then the average number of points earned per student over all the math classes is an example of a parameter.

One of the main concerns in the field of statistics is how accurately a statistic estimates a parameter. The accuracy really depends on how well the sample represents the population. The sample must contain the characteristics of the population in order to be a representative sample. In inferential statistics, we are interested in both the sample statistic and the population parameter.

Poll

Investigate

This section will be used to gain practice in reading through studies and gaining an understanding of the data presented. If we can identify the population, sample, parameter, statistic, and examples of data in the study, it can help understand and analyze the data. We will go over three examples.

Example 1: Determine what the key terms refer to in the following study:

1. Population           2. Sample          3. Parameter            4. Statistic              5. Data

We want to know the average amount of money first year college students spend at ABC College on school supplies that do not include books. We randomly surveyed 100 first year students at the college. Three of those students spent $150, $200, and $225, respectively.

1. The population is all first year students attending ABC College.

2. The sample is the 100 randomly selected first year students.

3. The parameter is the average amount of money spent excluding books by first year college students at ABC College this term.

4. The statistic is the average amount of money spent excluding books by first year college students in the 100 randomly selected first year students.

5. The data are the dollar amounts spent by the first year students. Examples of the data are $150, $200, and $225.

Example 2: Determine what the key terms refer to in the following study:

1. Population           2. Sample            3. Parameter           4. Statistic            5. Data

As part of a study designed to test the safety of automobiles, the National Transportation Safety Board collected and reviewed data about the effects of an automobile crash on test dummies. We want to know the proportion of dummies in the driver’s seat that would have had head injuries, if they had been actual drivers. We start with a simple random sample of 75 cars.

If you feel comfortable, try this exercise first before reviewing the answers.

1. The population is all cars containing dummies in the front seat.

2. The sample is the 75 cars, selected by a simple random sample.

3. The parameter is the proportion of driver dummies who would have suffered head injuries in the population.

4. The statistic is the proportion of driver dummies who would have suffered head injuries in the sample of 75 cars..

5. The data are either: yes, the dummy had head injury or no, it did not.

Example 3: Determine what the key terms refer to in the following study:

1. Population            2. Sample             3. Parameter            4. Statistic             5. Data

An insurance company would like to determine the proportion of all medical doctors who have been involved in one or more malpractice lawsuits. The company selects 500 doctors at random from a professional directory and determines the number in the sample who have been involved in a malpractice lawsuit.

Try the problem before reviewing the answers.

1. The population is all medical doctors listed in the professional directory.

2. The sample is the 500 doctors selected at random from the professional directory.

3. The parameter is the proportion of medical doctors who have been involved in one or more malpractice suits in the population.

4. The statistic is the proportion of medical doctors who have been involved in one or more malpractice suits in the sample.

5. The data are either: yes, was involved in one or more malpractice lawsuits or no, was not.