the table shows the mean monthly temperature in alcudia

The Mean from a Frequency Table

It is easy to estimate the Mean:

Supply aweigh each the numbers,
past divide by how many numbers game there are.

Example: What is the Mean of these numbers?

6, 11, 7

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

The Mean is 8

But sometimes we don't have a simple number of numbers, it power represent a frequency table like this (the "frequency" says how often they pass):

Score	Frequency
1	2
2	5
3	4
4	2
5	1

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

We could leaning wholly the numbers like this:

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

But rather than do lots of adds (like-minded 3+3+3+3) it is easier to use multiplication:

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

And rather than count how umpteen numbers there are, we can add up the frequencies:

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

And now we depend:

Beggarly = 2 + 10 + 12 + 8 + 5 14
= 37 14   =2.64...

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

Here is another example:

Model: Parking Spaces per House in Hampton Street

Isabella went finished and low the street to find out how many parking spaces each house has. Here are her results:

Parking Spaces	Frequency
1	15
2	27
3	8
4	5

What is the nasty number of Parking Spaces?

Answer:

Mingy = 15×1 + 27×2 + 8×3 + 5×4 15 + 27 + 8 + 5

= 15 + 54 + 24 + 20 55

= 2.05...

The Mean is 2.05 (to 2 decimal places)

(much easier than adding all Numbers separately!)

Notation

Now you get it on how to ut information technology, get's do that last deterrent example again, simply using formulas.

This symbol (named Sigma) means "sum up" (say more at Sigma Notation)

So we can say "tall altogether frequencies" this way of life:

(where f is frequency)

And we can utilise it suchlike this:

Likewise we can add heavenward "oftenness times score" this way:

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

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

The x with the bar on top off says "the mean of x"

So directly we are quick to Doctor of Osteopathy our model above, but with set note.

Model: Calculate the Nasty of this Frequency Table

x	f
1	15
2	27
3	8
4	5

And hither it is:

x = Σfx Σf = 15×1 + 27×2 + 8×3 + 5×4 15+27+8+5
= 2.05...

On that point you go! You hindquarters use sigma notation.

Bet in the Set back

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

Example: (continued)

From the previous good example, calculate f  × x in the right-hand chromatography column and then manage totals:

x	f	fx
1	15	15
2	27	54
3	8	24
4	5	20
TOTALS:	55	113

And the Mean is and then easy:

Mean = 113 55 = 2.05...

the table shows the mean monthly temperature in alcudia

Source: https://www.mathsisfun.com/data/mean-frequency-table.html