Study Guide

# Quantitative Data and Probability Introduction

## Quantitative Data and Probability Introduction

• There are three kinds of lies: lies, outrageous lies, and statistics.
• 98% of all statistics are made up.
• Statistics can be made to prove anything—even the truth.

We've heard all of these, and more, a thousand times before. In this lesson, though, we're going to stand up for statistics. It's the collection and analysis of data, especially quantitative data. Y'know, stuff that can be measured and verified.

Sure, it can be abused and misused, but it can also answer questions nothing else can. How many people worldwide are taller than Leonardo DiCaprio? Could we win an election for president? How much wood can woodchucks chuck? These are life's burning questions.

Before we get to the stats, though, we'll beef up our probability toolkit by finding expected values for events. Then we'll take a look at the data distribution superstar, the normal distribution. Then we'll finally look at how to collect and analyze data the right way.

By the end of all this, you'll be saying, "I love statistics almost as much as I love Shmoop. I'm going to send them a thank-you card and a sack of money." Okay, maybe you won't send us a card.

## Quantitative Data and Probability Resources

### Websites

wikiHow—How to Calculate an Expected Value
What did you expect, another explanation of finding the expected value? Well, that's what we've got here. Sorry if we surprised you with it.

Standard Deviation
The standard deviation just wants to help us estimate the variation in a sample. That, and to compete as an Olympic figure skater. We think it should just stick to what it's good at.

Math Is Fun—Normal Distribution
More bell-shaped curves than most people can shake a stick at. Only professional stick-shakers should even attempt it.

### Videos

Numberphile—Random Numbers
Picking a random number is tough. But if you love numbers enough, you'll use radiation to track some down.

JB Statistics—Sampling Distributions: Introduction to the Concept
Shmoop, meet the sampling distribution. Sampling distribution, this is Shmoop. Now that the introductions are out of the way, we think you'll have a lot in common.

Using a Z-score Table
Standard normal tables (or Z-score tables, as they are sometimes known) can be confusing. Maybe a wacky example or two will help?

Club Academia—Areas in between
The area between two points on a normal distribution—is there any space scarier? Other than under your bed, obviously.

### Games and Tools

Random.org
This website uses atmospheric noise to generate random numbers. Interestingly, the first prototype for this website used radio static to pick up atmospheric noise. If you ever need to run a lottery for your school or job, this is the site to use.

Interactive—Plop It!
Graphing our data makes it look pretty, but it takes so long to do by hand. Who has that kind of time? Use this to see where your data falls, and get the mean, median, and mode in a flash, too.

Online Stat Book—Sampling Distribution
Start with a normally distributed dataset. Then, pull a sample out and calculate an estimate. Then do it again and again. See it happen in real time by clicking this link, and then the Begin button to the left. We like watching each data point as it falls into place.

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