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# Probability and Statistics

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# Probability and Statistics Exercises

#### Qualitative v. Quantitative Data

There are two general types of data. Quantitative data is information about quantities; that is, information that can be measured and written down with numbers. Some examples of quantitative data a...

#### Categorical Data

One other type of data you'll need to know is categorical data. This is data that can be organized into mutually exclusive categories. If we look at a bunch of bananas and they're all either green,...

#### Discrete v. Continuous Data

Whenever we collect data, there's a collection of possible values from which we record our observations. If we're flipping a coin, the possible values we can observe are H (heads) or T (tails). Or,...

#### Univariate v. Bivariate Data

Before we start analyzing, we need to make one more distinction between different types of data. Then our data can take a seat on the couch and we'll start getting to the root of its daddy issues.S...

#### Range

Let's start with something near and dear to everyone's heart: test scores. Suppose ten students took a math test and received the following scores:61, 90, 72, 100, 80, 84, 88, 92, 92, 78.It's diffi...

#### Mode

The phrase "a la mode," used today to mean "with ice cream," literally means "in the fashion." As we know, there is nothing more fashionable than ice cream. In statistics, the mode of a set of data...

#### Mean/Average

When thinking about averages we like to think about cookies. Okay, we always like to think about cookies...averages are only a convenient excuse.Suppose Paul got 3 cookies and Mary got 5. That dist...

#### Median

The median of a list of numbers is the "middle" number. To find the median, first we put our list of numbers in order. Then we cross off pairs of numbers (one from the top of the list and one from...

#### Quartiles

Quartiles are numbers that break a list of data up into quarters ("quarters,'' "quartiles''... makes sense, right?). We are totally stuffed full of cookies at the moment, so let's turn our attentio...

#### Stem and Leaf Plots

A stem is something from which stuff grows. We can think of a digit like a stem: if we write down a single digit, each choice for the digit we write next "grows'' us a new number. If it doesn't see...

#### Bar Graphs and Histograms

Remember the difference between discrete and continuous data: discrete data has clear separation between the different possible values, while continuous data doesn't. We use bar graphs for displayi...

#### Pie Charts/Circle Graphs

Pie Charts, also known as circle graphs, are ways of displaying the proportions, or percentages, of data that fall into different categories. It makes sense that these graphs are useful for display...

#### Box and Whisker Plots

A box and whisker plot for a list of numbers is a picture built on a number line that uses five numbers: the lowest and highest values in the list, and the quartiles Q1, Q2, Q3. Try not to shave fo...

#### Scatter Plots

A common way of displaying bivariate data when both variables are quantitative is using a scatter plot. A scatter plot has a title, axes with labels, and (exactly like it sounds) little dots scatte...

#### Linear Regression

As we mentioned earlier, sometimes the dots in a scatter plot cluster like they're trying to make a nice shape. Sometimes the dots try to look like a straight line:Sometimes the dots try to look li...

#### Outcomes and Events

Whenever we do an experiment like flipping a coin or rolling a die, we get an outcome. For example, if we flip a coin we get an outcome of heads or tails, and if we roll a die we get an outcome of...

#### Important Elements

The probability of an eventis a fraction: is non-negative (that is, 0 or greater). There's no such thing as a negative number of outcomes. cannot be more than 1. There can't be more fa...

#### Odds

The probability of an event is written as a fraction:This probability tells us how likely an event is to happen.Odds are another way of conveying the same information, or another way of saying how...

#### Compound Events

A compound event, not a riot that occurs on prison grounds, is an event that can be described in terms of simpler events.A compound event will often, but not always, involve multiple experiments. O...

#### Independent and Dependent Events

Suppose we have a jar with 10 pieces of chocolate candy and 5 pieces of vanilla candy. Clearly, the chocolate candy is far superior, which is why we went out and bought twice as many of them.We...

#### Mutually Exclusive Events

These are not parties that only mutual fund managers are allowed to attend. Don't worry; you aren't missing much. Not too much roof-raising goes on at those shindigs.
Sometimes two events...

#### Factorials and Permutations

Let's say we have two books: The Odyssey and The Iliad. We should probably have more books, but if we're only going to have two, these are a good two to have. There are two possible ways to order t...

#### Combinations

A combination is a selection of objects the order of which doesn't matter. If you order a combination meal from McDonald's, for example, it doesn't matter if you eat the soda, fries or burge...

#### More Probability

Now that we can find numbers of permutations and combinations, we can find more complicated probabilities.Sample ProblemA jar contains 5 vanilla candies, 9 spice candies, and 3 shrimp candies. That...