Results 1 to 5 of 5

Math Help - Please help me with coding, statistics? How do I do this?

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    uk
    Posts
    15

    Please help me with coding, statistics? How do I do this?

    I can find out the mean, but not S.D /variance. How can I do this? Please show your steps so that I can understand. Thank you


    A class of 20 students takes a test. The score, x, for each student was recorded by the teacher. The results are summarized by


    Σ(x-10) = 208 and Σ(x-10) = 2716

    (i) Calculate the standard deviation of the 20 scores.

    (ii) Show that Σx = 8876.


    (iii) Two other students took the test later. Their scores were 18 and 16. Find the mean and standard deviation of all 22 scores.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: Please help me with coding, statistics? How do I do this?

    Quote Originally Posted by emily9843 View Post
    I can find out the mean, but not S.D /variance. How can I do this? Please show your steps so that I can understand. Thank you


    A class of 20 students takes a test. The score, x, for each student was recorded by the teacher. The results are summarized by


    Σ(x-10) = 208 and Σ(x-10) = 2716

    (i) Calculate the standard deviation of the 20 scores.

    (ii) Show that Σx = 8876.


    (iii) Two other students took the test later. Their scores were 18 and 16. Find the mean and standard deviation of all 22 scores.
    Hi emily9843!

    Can you expand Σ(x-10) = 208 in terms of Σx?
    And can you also expand Σ(x-10) = 2716 in terms of Σx and Σx?

    Which formulas do you have for the standard deviation or variance?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2013
    From
    uk
    Posts
    15

    Re: Please help me with coding, statistics? How do I do this?

    Hi, I found out how to do the SD. I did this by working the mean and sd out for y and then adding 10 for the mean of x. However, I am not sure how to do ii and iii. I'm so confused Thank you
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: Please help me with coding, statistics? How do I do this?

    Let's take a look at Σ(x-10) = 208.

    If we expand this, we get:

    \sum(x-10) = \sum_{i=1}^{20} (x_i - 10) = (x_1 - 10) + (x_2 - 10) + (x_3 - 10) + ... + (x_{20} - 10)

    Rearranging the terms we get:

    \sum(x-10) = (x_1 + x_2 + x_3 + ... + x_{20}) - (10 + 10 + 10 + ... + 10)

    Now we make it more compact again:

    \sum(x-10) = (\sum_{i=1}^{20} x_i) - 20 \times 10 = \sum x - 200


    So we have:

    Σ(x-10) = Σx - 200 = 208

    Σx = 208 + 200 = 408


    Can you do something similar for Σx?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Feb 2013
    From
    Saudi Arabia
    Posts
    439
    Thanks
    86

    Re: Please help me with coding, statistics? How do I do this?

    Hi Miss EMILY

    please follow the following steps.

    1. divide 208 by 20 to find 10.4 this is the so called the modified mean of the dataset.
    then add 10 which is the number you subtract from every data of the data set and the real mean of the data set is 20.4

    2. to find the SD use the following formulae: SD=SQROOT(2716/20 -(10.4)^2) and then SD = sqrroot(135.8-108.16)=sqrroot(27.64)=5.25

    unlike the mean which depends on the number that you subtract or you add ( modified mean ) the standard deviation remains the same for the real values of x or (x-k) or (x+k)...therefore
    to find the Σχ^2 use the following formula: (SD)^2=(Σχ^2)/20-(20.4)^2. Substitute SD=5.25 and make Σχ^2 the subject of the formula...you must find ...Σχ^2=967.41.

    Νοw to find the new mean and SD of the 22 students works as follows.
    first use the modified data and subtract from each new data the number 10. therefore (18-10) +(16-10) =14

    ADD 14 + Σ(χ-10) to find 222 and divide this number by 22 to find the new modified mean =222/22=10.09
    this is the new modified mean for the 22 students and the real mean is 10.09 +10 =20.09

    to find the new standard deviation you need to add (18-10)^2 +(16-10)^2 to the old summ 2716 to find 2716+100=2816.

    then use the same formula for the standard deviation as above to find SD=SQRROOT(2816/22-(10.09)^2 AND YOU MUST FIND SD=SQRROT(26.1919)=5.117

    THIS IS THE NEW STANDARD DEVIATION FOR THE 22 STUDENTS.

    GOOD LUCK
    MINOAS
    Please check and verify all the calculations for any typing mistake.....
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Coding Theory
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: October 11th 2012, 06:36 PM
  2. Coding method
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 16th 2009, 12:36 PM
  3. coding method
    Posted in the Statistics Forum
    Replies: 1
    Last Post: July 23rd 2009, 11:32 AM
  4. Coding theory question
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 13th 2008, 05:31 PM

Search Tags


/mathhelpforum @mathhelpforum