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  • This lesson will introduce you to the three measures of central tendency.

  • Don’t be scared by the terminology; we are talking about mean, median and mode.

  • ? Even if you are familiar with these terms, please stick around, as we will explore their

  • upsides and shortfalls.

  • Ready?

  • Let’s go.

  • The first measure we will study is the mean, also known as the simple average.

  • It is denoted by the Greek letter mu for a population and x bar for a sample.

  • These notions will come in handy in the next section.

  • We can find the mean of a data set by adding up all of its components and then dividing

  • them by the number of components contained in the data set.

  • The mean is the most common measure of central tendency but it has a huge downsideit

  • is easily affected by outliers.

  • Let’s compare these two data sets.

  • These are the prices of pizza at 11 different locations in New York City and 10 different

  • locations in LA.

  • Let’s calculate the means of the two datasets using the formula.

  • For the mean in NYC, we get 11 dollars, whereas for LA - just 5.5!

  • On average, pizza in New York can’t be twice as expensive as in LA, right?

  • Correct.

  • ? The problem is that in our sample, we have included one posh place in New York,

  • where they charge 66 dollars for pizza, and this doubled the mean.

  • What we should take away from this example is that the mean is not enough to make definite

  • conclusions.

  • So, how can we protect ourselves from this issue?

  • You guessed it, we can calculate the second measurethe median.

  • The median is basically themiddlenumber in an ordered data set.

  • Let’s see how it works for our example.

  • In order to calculate the median, we have to order our data in ascending order.

  • The median of the data set is the number at position n plus 1, divided by two in the ordered

  • list, where n is the number of observations.

  • Therefore, the median for NYC is at the sixth position or $6.

  • Much closer to the observed prices than the mean of $11, right?

  • What about LA?

  • We have just 10 observations in LA.

  • According to our formula, the median is at position 5.5.

  • In cases like this, the median is the simple average of the numbers at positions 5 and

  • 6.

  • Therefore, the median of LA prices is 5.5 dollars.

  • Okay, we have seen that the median is not affected by extreme prices, which is good

  • when we have posh New York restaurants in a street pizza sample.

  • But we still don’t get the full picture.

  • Are the majority of restaurants low cost or average?

  • We must introduce another measurethe mode.

  • The mode is the value that occurs most often.

  • It can be used for both numerical and categorical data, but we will stick to our numerical example.

  • After counting the frequencies of each value, we find that the mode of New York pizza prices

  • is 3 dollars.

  • Now, that’s interesting!

  • The most common price of pizza in NYC is just 3 dollars, but the mean and median led us

  • to believe it was much more expensive.

  • Ok, let’s do the same and find the mode of LA pizza prices.

  • Hmmeach price appears only once.

  • How do we find the mode then?

  • Well, we say that there is no mode.

  • But can’t I say that there are 10 modes, you may ask?

  • Sure you can, but it will be meaningless with 10 observations and an experienced statistician

  • would never do that.

  • In general, you often have multiple modes.

  • Usually two or three modes are tolerable, but more than that would defeat the purpose

  • of finding a mode.

  • There is one last question that we haven’t answered.

  • Which measure is best?

  • The NYC and LA example shows us that measures of central tendency should be used together

  • rather than independently.

  • Therefore, there is no best, but using only one is definitely the worst.

  • ? Alright, now you know about the mean, median

  • and mode.

  • In our next video, we will use that knowledge to talk about skewness.

  • Stay tuned and thanks for watching!

This lesson will introduce you to the three measures of central tendency.

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統計学のチュートリアル.平均、中央値、モード (Statistics Tutorials: Mean, median and mode)

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    林宜悉 に公開 2021 年 01 月 14 日
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