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Formulating a mean formula

  1. Nov 28, 2016 #1
    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

    jOQRNgZ.jpg


    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. jcsd
  3. Nov 28, 2016 #2

    Mark44

    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.
     
  4. Nov 28, 2016 #3
    Thanks for reply.

    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?
     
  5. Nov 28, 2016 #4

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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}##
     
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