Add the numbers: 6 + 11 + 7 = 24Divide by how many numbers (there are 3 numbers): 24 ÷ 3 = 8

### The Mean is 8

But sometimes we don"t have a simple menu of numbers, it might be a frequency table lượt thích this (the "frequency" says how often they occur):

ScoreFrequency
12
25
34
42
51

(it says that score 1 occurred 2 times, score 2 occurred 5 times, etc)

We could menu all the numbers like this:

Mean = 1+1 + 2+2+2+2+2 + 3+3+3+3 + 4+4 + 5(how many numbers)

But rather than bởi lots of adds (like 3+3+3+3) it is easier lớn use multiplication:

Mean = 2×1 + 5×2 + 4×3 + 2×4 + 1×5(how many numbers)

And rather than count how many numbers there are, we can showroom up the frequencies:

Mean = 2×1 + 5×2 + 4×3 + 2×4 + 1×52 + 5 + 4 + 2 + 1

And now we calculate:

Mean = 2 + 10 + 12 + 8 + 514 = 3714 = 2.64...

Bạn đang xem: Fx

And that is how to lớn calculate the mean from a frequency table!

Here is another example:

### Example: Parking Spaces per House in Hampton Street

Isabella went up & down the street to lớn find out how many parking spaces each house has. Here are her results:

ParkingSpacesFrequency
115
227
38
45

What is the mean number of Parking Spaces?

Mean=15×1 + 27×2 + 8×3 + 5×415 + 27 + 8 + 5
=15 + 54 + 24 + 2055
=2.05...

The Mean is 2.05 (to 2 decimal places)

(much easier than adding all numbers separately!)

## Notation

Now you know how to vì it, let"s do that last example again, but using formulas.

 This symbol (called Sigma) means "sum up" (read more at Sigma Notation)

So we can say "add up all frequencies" this way:

(where f is frequency)

And we can use it lượt thích this:

Likewise we can địa chỉ up "frequency times score" this way:

(where f is frequency & x is the matching score)

And the formula for calculating the mean from a frequency table is:

The x with the bar on đứng đầu says "the mean of x"

So now we are ready to bởi vì our example above, but with correct notation.

### Example: Calculate the Mean of this Frequency Table

xf
115
227
38
45

And here it is:

x = ΣfxΣf = 15×1 + 27×2 + 8×3 + 5×415+27+8+5= 2.05...

There you go! You can use sigma notation.

Xem thêm: Hình Học 12 Bài 2: Phương Trình Mặt Phẳng, Phương Trình Mặt Phẳng Trong Không Gian

## Calculate in the Table

It is often better to do the calculations in the table.

### Example: (continued)

From the previous example, calculate f × x in the right-hand column và then bởi vì totals: