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):
| 1 | 2 |
| 2 | 5 |
| 3 | 4 |
| 4 | 2 |
| 5 | 1 |
(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...
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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:
| 1 | 15 |
| 2 | 27 |
| 3 | 8 |
| 4 | 5 |
What is the mean number of Parking Spaces?
Answer:
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:
And we can use it lượt thích this:
Likewise we can địa chỉ up "frequency times score" this way:
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
| 1 | 15 |
| 2 | 27 |
| 3 | 8 |
| 4 | 5 |
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.
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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: