Why is the mean important?

We looked before at the shoe sales information in this table.

Let’s review how to find the mean.

We divide the total of the data, four hundred fourteen…

…by the total number of weeks, nine.

The quotient, forty-six, is the mean.

We see that the mean is forty-six.

We also learned that it is easier to work with the data in this table…

…if we organize it from smallest to largest.

Let’s look at just the number of pairs of shoes sold.

We know that the minimum is thirty-one…

…and the maximum is fifty-seven.

The number in the middle is called the median.

This means that half of the data is below the median…

…and half is above the median.

We can also find the median when we have an even set of numbers We can also find the median when we have an even set of numbers. This set of data is organize from smallest to largest.

To find the median, we start at the smallest and largest numbers…

…and work our way in…

…towards the middle.

When we have an even set of numbers, the median is halfway between the two middle numbers. What number is halfway between one hundred ten and one hundred twenty?

The median is one hundred fifteen.

Let’s look at another even set of numbers.

Here, the two numbers in the middle are the same Here, the two numbers in the middle are the same. What do you think the median is for this set?

If the two numbers in the middle are the same, both numbers are the median. Here, the median is three hundred eighty-five.

How do we present the data to find the mean and the median? 25

This table shows the heights of students in a class, ordered from low to high. 26

To find the mean, we need to divide the total inches by the total number of students. 27

The total of the inches is one thousand, five hundred thirty. 28

We divide by the number of students, twenty-three… 29

…to find the mean. 30

The mean of this data is sixty-six and five tenths, or sixty-six and one half, inches. 31

Now we’ll find the median. 32

We need to find the middle point in the list. 33

We count from both ends until we reach the middle… 34

…and we see that the median is sixty-eight inches. 35

When we have a long list of data, it is sometimes easier to organize it into a tally chart, like this one. Each X represents the height of one student. 36

To find the mean, we divide the total inches, one thousand five hundred thirty… 37

…by the number of students, twenty-three. 38

Again, we see that the mean… 39

…is sixty-six and one half inches. 40

To find the median, we start with the smallest and largest values… 41

…then the next smallest and largest… 42

…until we reach the number in the middle. 43

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We stop crossing off numbers when we reach the middle. 51

This is the median. 52

We see that the median for this set of data is sixty-eight inches. 53