Definition of Statistics: the Science of Collecting, Displaying, and Using Data

Math 2311 Chapter One

Definition of statistic: A number calculated according to a formula or process that is used to describe or infer information. A statistic is created using numbers from a collection of data

Definition of statistics: The science of collecting, displaying, and using data

Uses of statistics: description and inference

 Description how tall, how fast, what pattern graphs Often a summary of data

 Inference what might happen, what is next estimates and predictions, decisions about a matter

Statistical Basics

Vocabulary matters

Population

Variable

Sample

Inference

Measure of reliability

Type of data Example One

A national water expert is interested in determining the average amount of lead in ppm (parts per million) that is found in Houston, Texas drinking water. She considers only residential households within the city limits. She collects samples from 1200 randomly selected homes and runs tests on each sample. In her final report, she states that she has 90% confidence that the drinking water in Houston contains lead in the amount of between 25 and 100 ppm.

This is an example of a statistical inference

Population

Variable

Sample

Type of data

Inference

Measure of reliability Example Two

One of the largest and most expensive experiments in history was carried out in the mid 50’s…a million children at a cost of over 5 million dollars were vaccinated against poliomyelitis…the vaccine was deemed effective because among the children vaccinated the frequency of polio diagnosed was half the number than the cases diagnosed among the unvaccinated. The investigators inferred that vaccinating all children would cut down the incidence of disease by 50%  3%. (source: Dietrich and Kearns, Basic Statistics)

Population

Variable

Sample

Type of data

Inference

Measure of reliability Example Three

After examining the medical records for 1000 patients of the Baylor Family Clinic on Kirby, investigators estimate that about 30% of all illnesses are psychosomatic in origin. In fact, their report states that the investigators are 99% sure that between 26% and 34% of all illnesses treated by physicians at the clinic are psychosomatic in origin. (source: Dietrich and Kearns, Basic Statistics)

Population

Variable

Sample

Type of data

Inference

Measure of reliability Example 4

In 1789, the English scientist Henry Cavendish measured the density of the earth with great care – he performed his experiment 29 times. He concluded that the earth is between 5.22 and 5.66 times denser than water; he was 90% sure that he was right (source: David S Moore: The Basic Practice of Statistics)

Population

Variable

Sample

Type of data

Inference

Measure of reliability