20250303 What is Statistics? Introduction

1: Statistical Basics

What is Statistics? 

Statistics is the study of how to collect, organize, analyze, and interpret data collected from a group. (Kozak, 2021)

Terms:

source : https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Statistics_with_Technology)

Many find Population and Sample confusing, in order to remember the difference sample is simply just the subset from population.

Population – set of all values of the variable for the entire group of individuals.

Sample – a subset from the population. It looks just like the population, but contains less data

Image from: https://miro.medium.com/v2/resize:fit:1400/1*83WLnE2QTeOHSjbPJDVKfw.png


Image from (click here): 1.1: What is Statistics? - Statistics LibreTexts 

I tried to answer the practice questions:

  1. Suppose you want to know how Arizona workers age 16 or older travel to work. To estimate the percentage of people who use the different modes of travel, you take a sample containing 500 Arizona workers age 16 or older. State the individual, variable, population, sample, parameter, and statistic. 

    Solution

    Individual – Arizona workers 

    Variable – different modes of travel

    Population – workers age 16 or older travel to work

    Sample –  sample containing 500 Arizona workers age 16 or older

    Parameter – percentage of Arizona workers age 16 or older who use the different modes of travel

    Statistic– percentage of 500 people who use the different modes of travel

  2. You wish to estimate the mean cholesterol levels of patients two days after they had a heart attack. To estimate the mean you collect data from  28 heart patients. State the individual, variable, population, sample, parameter, and statistic. 

    Solution

    Individual – heart patients

    Variable –  cholesterol levels of patients two days after they had a heart attack

    Population –  patients who have had heart attacks

    Sample –   heart patients

    Parameter – mean cholesterol levels of patients two days after they had a heart attack

    Statistic– mean cholesterol levels of heart patients

  3. State the measurement scale for each.
    1. Cholesterol level - Ratio
    2. Defect type - Nominal
    3. Time of first class - Interval
    4. Opinion on a 5 point scale, with 5 being strongly agree and 1 being strongly disagree - Ordinal
  4. State the measurement scale for each.
    1. Temperature in degrees Celsius - Interval
    2. Ice cream flavors available - Nominal
    3. Pain levels on a scale from 1 to 10, 10 being the worst pain ever - Ordinal
    4. Salary of employees - Ratio
OPINION and TIPS:

At first, the problem can seem confusing, especially when it comes to understanding the difference between population and sample. That's why answering practice exercises is helpful, practice makes perfect! (Also, be sure to read the problem carefully!) Additionally, while identifying the measurement scale is usually easy, I sometimes get confused between Interval and Ratio scales. To remember the difference, I keep in mind that the Interval scale has no true zero and can represent values below zero, whereas the Ratio scale never falls below zero

References:

Textbook: 

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