Lesson VIDEO: Mean and Standard Deviation Part 1

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About bperkhou: I am a student at Stanford University.

*[youtube vMa94EPjhsE]

In this lesson we will learn about the "mean" and "standard deviation." These are words used to describe "data" - so what are data? Here is an example. My older brother goes to school in the morning in his car, and I go on my bike. We recorded how many minutes it took us to get to school every day in this table:

*[illustration MandSD1_data.jpg]

This is what we call data. We have two variables: my times on the bike and my brother's on the car. They are called variables because every day they can be different (they vary). For example, on October 2nd, it took me 14 minutes to get to school compared to my brother's 18 minutes. But on the next day, it took me 18 minutes compared to his 10 minutes. Altogether, the variables and the values we recorded every day are called "data."

Now we are ready to talk about mean and standard deviation. To explain these concepts, I will use only part of the data I've shown you: the first 10 recorded days. This is the data we're working with:

*[illustration MandSD1_first_ten.jpg]

The mean is also called the average. The mean of the data is the usual time - what you would expect. For example, the mean of my times on the bike is not 13 or 19 because those are unusually low and high times. Looking at the times for these 10 days, we would usually expect it to take 16 minutes to get to school on bike. You can say "it takes around 16 minutes on average." This is exactly what the "mean" is - there is an exact mathematical formula for it which we will learn about in a different lesson. Now let's look at my brother's times with the car. The lowest times are 7 and 9, while the highest time is 23 minutes. The mean has to be somewhere in between - it's the usual time it takes to get to school with a car. We can see that most times are around 14 or 15 minutes. This indicates that 14 minutes is a pretty good guess for the mean time of getting to school in a car.

Now let's talk about standard deviation. We already know that the mean is the expected time to get to school - the standard deviation is how close we usually are to the mean, the expected time. For example, we already estimated that the mean time for me to get to school on my bike is about 16 minutes. The times vary from 3 minutes more than 16 to 3 less: but more are within 1 or 2 of 16, the mean. Thus, we estimate that the standard deviation is about 2. What this means is, I expect to get to school in 16 minutes on average (the mean), but most of the time I'll get to school within 2 minutes of the usual 16 (so between 14 and 18 minutes). Note, we're guessing what the standard deviation is based on the data, but there actually exists a precise mathematical formula that we'll learn about in another lesson. We can repeat the estimation with my brother's data. We believe that the mean is about 14 minutes. So how close are the data to 14? The highest and lowest values are 23 and 7 - they are 9 above 14 and 7 below. But there are also more times that are closer to 14, like 11, 12, 15, 16. Those are within 2 or 3 of 14. Then we would guess that usually, the time it takes to get to school is within 5 minutes of 14, the mean.

As I mentioned, there are formulas for the mean and standard deviation. But even without the formulas, the ideas are simple and our guesses are pretty good. Using a computer, I found that the mean bike time is 16.67 with standard deviation of 1.94. The mean car time is 14.33 with standard deviation 5.15. These are really close to our guesses (16, 2, 14, 5 in the same order).

To learn the formulas for mean and standard deviation, read and watch the next parts of this lesson!