# Formulating a mean formula

1. Nov 28, 2016

### random39a

1. The problem statement, all variables and given/known data

I'm trying to formulate a formula based on an experiment I did.

2. Relevant equations

3. The attempt at a solution

where

x_1 = mean (one of 5 mean values)
x_i = value of variables (there are 4 of them added together)
n = number of variables

My problem is, for the left hand side of the formula, I want to show that there are 5 means, so x_1 to x_5 = the right hand side as shown

I'm not sure how to show this mathematically.

Wonder if anyone might be able to help.

Thanks.

Last edited by a moderator: Nov 28, 2016
2. Nov 28, 2016

### Staff: Mentor

I don't understand what you're doing.
$x_1$ is one of the four values in your summation. $\bar{x_1}$ is the mean of the four values. Since your summation runs from 1 to 4, I assume you mean for n to be 4, not 5 as you seem to indicate.
With n = 4, we have $\bar{x_1} = (1/4)(x_1 + x_2 + x_3 + x_4)$
???
For the four numbers you're adding, there is only one mean.

3. Nov 28, 2016

### random39a

I'm just trying to let the person who reads the formula know that I have used this formula to calculate 5 mean values x_1, x_2, x_3, x_4 and x_5.

eg/

result number one x_1 of 5 results x_5

YELLOW

499

ORANGE

317

PURPLE

545

BLACK

110

AVERAGE

367.75

The data above is one of 5 sets of data for which I have to calculate the mean.

For this data, I calculated the mean using my formula x_1= 1/4 (Sum of Yellow, Orange, Purple, Black) = 367.5

I did this 4 more times with 4 other data sets just like this one.

Does this make sense what I'm trying to do?

4. Nov 28, 2016

### PeroK

You need something like:
$\bar{x}_i = \frac14 \sum_{j=1}^{4}x_{ij}$

Where $\bar{x}_i$ is the average of the $i$th set of data $x_{i1} \dots x_{i4}$