# Statistics

18.01.2019

Episode #10 of the course Everyday math by Jenn Schilling

Welcome to the final lesson of Everyday Math! I hope you’ve enjoyed learning about different math concepts and how they apply to our everyday lives! I’ve certainly enjoyed exploring this topic with you!

Today, in our last lesson, we will cover statistics.

The Math

Statistics is a broad topic that involves the study and analysis of data. We’re going to cover a few key ideas in statistics so you’ll be able to better understand and consume information. So, what do you need to know?

First, it’s important to understand measures of center (mean, median, and mode). These metrics help us understand the central tendency of a dataset, or how the center of the data behaves. The mean tells us the average of the data, the median tells us the middle, and the mode is the most frequent number in the data. The range is another important statistic; it tells us the spread of the data, or the distance between the largest and the smallest numbers in the dataset. These four statistics help us understand the shape of the dataset. If the mean and the median are close together, then the dataset is similar to a normal distribution, or a bell curve, in which most of the data is clustered around the middle.

Much of statistics concerns hypothesis testing. The hypothesis is a theory about a group of data. Hypothesis testing is the process of drawing and testing conclusions about the data. Using statistical testing, a hypothesis can be proven true or false. Usually, a t-test (a statistical test that helps us determine whether there is a significant difference between two groups of data) and p-values are used to prove or disprove a hypothesis by comparing the actual data to a statistical distribution that would represent the data if the hypothesis were true. The p-value tells us the probability of achieving our data or more extreme if the null hypothesis is true (if the p-value is large enough, the statistical test [the t-test] has proven that there is a significant difference, which implies that the null hypothesis is not true). The null hypothesis is what we want to disprove with a hypothesis test.

Another important topic to understand in statistics is correlation. Correlation describes the relationship between two variables. The closer the correlation is to 1, the stronger the relationship between the variables. A positive correlation indicates a positive relationship (when one variable increases, so does the other); a negative correlation indicates a negative relationship (when one variable increases, the other decreases). Of course, the most important thing to understand about correlation is that correlation does not imply causation. Frequently, correlation and causation are conflated. However, simply because two variables are correlated does not mean that one causes the other.

Regressions tell us how variables are related and if one does indeed cause another. A regression is basically a technique for creating an equation from a group of data. The regression tells us if we can draw conclusions from the data about how the variables are related and affect one another. For example, if we have data on education level, zip code, race, and income, we could use a regression to determine if race, zip code, and income have an effect on education level.

Everyday Applications

Statistics are everywhere! We see them in sports, news articles, and scientific studies. As computers get more powerful and the amount of data available increases, statistical analyses are becoming more prevalent in our everyday lives.

Whether it’s predictions about elections or sports, statistics and probability are used to draw conclusions. Statistical distributions and hypothesis testing play a big role in these kinds of predictions. Sports statistics also tell us players’ averages that represent their abilities and likely future performance.

When consuming the news or popular science, it is important to understand basic statistics so you’re able to accurately interpret information. Remember that correlation and causation are separate when consuming statistical information, and pay attention to the assumptions made in a study.

I sincerely hope that you’ve enjoyed this Everyday Math course! Math is a fascinating subject and understanding it can be fun! It’s important to have a basic understanding of math concepts!

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