How do we use statistics to make sense of data?

We’ve learned about different ways to look at data We’ve learned about different ways to look at data. We need to look at all of the numbers – mean, median, min, max, and range – to have a good understanding of a set of data.

The table shows the minimum, twenty-one…

…and the maximum, forty-seven.

The range, or difference between the max and min, is twenty-six.

The mode, or the number that appears most often, is twenty-nine.

To find the mean, we divide the total, three hundred twenty-four…

…by the number of weeks, nine.

We see that the mean is thirty-six.

The median, or number in the middle, is thirty-eight.

In this case, the mean and the median are close In this case, the mean and the median are close. Either one is a good indication of what’s “about average.”

Let’s look at another set of data.

Here we see the minimum is one…

…and the maximum is one hundred three.

The median is halfway between the numbers in the middle The median is halfway between the numbers in the middle. What is halfway between eighty-three and eighty-five?

The median is eighty-four.

To find the mean, we divide the total, five hundred forty-four…

…by the number of weeks, eight.

The quotient is sixty-eight…

…so we see that the mean is sixty-eight.

Notice that there is a big difference between the median and the mean.

Look at the numbers one and seven Look at the numbers one and seven. How do they compare to the rest of the numbers?

We see that they are much smaller than the other numbers in the set.

We call these numbers outliers We call these numbers outliers. An outlier is any number that is significantly smaller or larger than the other numbers in the set.

Let’s see what happens when we remove the one and seven Let’s see what happens when we remove the one and seven. Now our minimum is seventy-eight…

…and the maximum is still one hundred three.

The median is halfway between eighty-five and ninety-two The median is halfway between eighty-five and ninety-two. It is eighty-eight and one half.

To find the mean, we divide the new total, five hundred thirty-six…

…by the number of weeks, six.

The mean is eighty-nine and three tenths.s

Notice that the mean and median are now much closer.

Let’s change the data slightly Let’s change the data slightly. Suppose that instead of selling one car during the week of September 24th, we sold one thousand cars.

Let’s see what this very large number does to our data.

The total is much larger. What do you think this will do to the mean?

We see that the median is still eighty-eight and one half…

…but the mean has increased to one hundred ninety-two and nine tenths.

We see that the mean and median are not close We see that the mean and median are not close. The median is a much better description of this data.

It’s important to remember that when the mean and median are close, either number is a good description of the center of the data.

When they are far apart, the median tends to be a better description of the center of the data.