# Need help with the Mean formula

#### Inferno

##### New member
I thought I understood the formula, but I can't figure out how to set it up for this problem.

#### stapel

##### Super Moderator
Staff member
I thought I understood the formula, but I can't figure out how to set it up for this problem.
Which formula? What did you plug in, where? Where did you get stuck?

#### Subhotosh Khan

##### Super Moderator
So now tell us what did you plug in? what did you get?

#### Inferno

##### New member
I am pretty sure I plugged the stuff in wrong. here's what I did for Set A

E20/6 = 5x10
E3.3 = 50
E=15.1

and set B

E20/6 = 50x10
E3.3=500
E=151.5

#### Subhotosh Khan

##### Super Moderator
I am pretty sure I plugged the stuff in wrong. here's what I did for Set A

E20/6 = 5x10
E3.3 = 50
E=15.1

and set B

E20/6 = 50x10
E3.3=500
E=151.5
Okay that is not the way to work with mean (or average).

Tell us the definition of mean (or average).

#### Inferno

##### New member
mean is when you add all the numbers up and divide by how many there are

#### Inferno

##### New member
10+20/6 = Set A is 5?

and 500+20/6= Set B is 86.7 ? are those right? I did that without the formula because the formula confuses me.

#### JeffM

##### New member
10+20/6 = Set A is 5?

and 500+20/6= Set B is 86.7 ? are those right? I did that without the formula because the formula confuses me.
The formula is not confusing. The problem is confusingly worded because it changes the definitions of the sets.

For set $$\displaystyle A = \{x_1,\ x_2,\ x_3,\ x_4,\ x_5\}.$$

$$\displaystyle \displaystyle \bar x_A = \dfrac{\displaystyle \sum_{i=1}^5x_i}{5} = 10 \implies\sum_{i=1}^5x_i = 5 * 10 = 50.$$ Follow that?

Now let's define a new set $$\displaystyle H = \{x_1,\ x_2,\ x_3,\ x_4,\ x_5\, x_6\},\ where\ x_6 = 20.$$

So $$\displaystyle \displaystyle \bar x_H = \dfrac{\displaystyle \sum_{i=1}^6x_i}{6}.$$ Still using the formula.

But what is the numerator in that formula equal to?

Here is the trick

$$\displaystyle \displaystyle \sum_{i=1}^6x_i = \left(\sum_{i=1}^5x_i\right) + x_6.$$ Does that make sense?

And we know what the two terms on the right of the equation equal.

$$\displaystyle \displaystyle \sum_{i=1}^6x_i = 50 + 20 = 70 \implies \bar x_H = \dfrac{70}{6} \approx 11.67$$

Now try the second problem on your own, and let us know what you get.

50x10= 500

500+20= 520

520/6 = 86.7

still wrong? lol

#### Subhotosh Khan

##### Super Moderator
50x10= 500

500+20= 520

520/6 = 86.7

still wrong? lol
In the third line - why are you dividing by '6'?

You started 50 data points (n = 50) - you added one more. How many data points do you have now?

#### Inferno

##### New member
oh I guess I was looking at the 6 from Set A.

so

51x10= 510

510+20= 530

530/51 = 10.4?

#### Subhotosh Khan

##### Super Moderator
oh I guess I was looking at the 6 from Set A.

so

51x10= 510

510+20= 530

530/51 = 10.4?
Still wrong .... you are not thinking straight:

old sum → 50 * 10 = 500

new sum → 500 + 20 = 520

New average = 520/51 = 10.196