The Mean from a Frequency Table

Information technology is piece of cake to calculate the Mean:

Add together up all the numbers,
and so divide by how many numbers there are.

Example: What is the Hateful of these numbers?

half-dozen, 11, 7

  • Add the numbers: 6 + eleven + 7 = 24
  • Divide by how many numbers (there are 3 numbers): 24 ÷ 3 = viii

The Mean is 8

Simply sometimes we don't have a simple listing of numbers, it might be a frequency table like this (the "frequency" says how often they occur):

Score Frequency
i 2
2 five
three 4
iv 2
5 ane

(information technology says that score 1 occurred two times, score two occurred 5 times, etc)

We could listing all the numbers like this:

Mean = one+1 + 2+two+ii+2+ii + three+3+3+three + four+4 + v (how many numbers)

But rather than do lots of adds (like 3+three+3+iii) it is easier to utilize multiplication:

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

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

Mean = 2×1 + 5×ii + 4×three + two×4 + 1×5 2 + 5 + 4 + 2 + one

And now we summate:

Mean = 2 + 10 + 12 + eight + five 14
= 37 14   =2.64...

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

Hither is some other example:

Example: Parking Spaces per House in Hampton Street

Isabella went upwardly and down the street to discover out how many parking spaces each business firm has. Here are her results:

Parking
Spaces		 Frequency
1 xv
two 27
3 eight
4 five

What is the mean number of Parking Spaces?

Answer:

Mean = 15×ane + 27×2 + eight×3 + 5×4 15 + 27 + 8 + v

= 15 + 54 + 24 + 20 55

= two.05...

The Mean is ii.05 (to 2 decimal places)

(much easier than adding all numbers separately!)

Notation

At present you know how to do it, let'south do that last example again, only using formulas.

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

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

sum f
(where f is frequency)

And we can apply it similar this:

sum f

Likewise nosotros tin can add upward "frequency times score" this style:

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

And the formula for calculating the mean from a frequency tabular array is:

mean of a frequency table

The 10 with the bar on superlative says "the mean of x"

So now nosotros are ready to do our example above, but with correct notation.

Instance: Calculate the Hateful of this Frequency Table

ten f
one 15
2 27
3 8
four 5

And here it is:

x = Σfx Σf = 15×1 + 27×2 + 8×3 + v×iv xv+27+8+5
= two.05...

There you go! Yous can apply sigma note.

Calculate in the Table

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

Case: (continued)

From the previous instance, calculate f  × x in the right-mitt cavalcade and so practice totals:

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

And the Mean is then easy:

Mean = 113 55 = two.05...