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Math Help - Desperate Dissertation help: Likert scale analysis 1-5 and Standard Deviation

  1. #1
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    Desperate Dissertation help: Likert scale analysis 1-5 and Standard Deviation

    I've completely forgot how this works.

    Here's my table, could anyone please start me off with the std dev of some of these:



    Thanks in advance! In a pickle.
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  2. #2
    Super Member Aryth's Avatar
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    I'll do the Standard Deviation for Item 2:

    1: Find arithmetic mean:

    \frac{(1 + 6 + 5 + 8 + 4 + 7)}{6} = \frac{31}{6} = 5.1666667

    2. Find the deviation of each number from the mean:

    1 - 5.1666667 = -4.1666667 = -\frac{25}{6}

    6 - 5.1666667 = 1.1666667 = \frac{7}{6}

    5 - 5.1666667 = 0.1666667 = \frac{1}{6}

    8 - 5.1666667 = 3.1666667 = \frac{19}{6}

    4 - 5.1666667 = -1.1666667 = -\frac{7}{6}

    7 - 5.1666667 = 2.1666667 = \frac{13}{6}

    3. Square each Deviation:

    \left(-\frac{25}{6}\right)^2 = \frac{625}{36}

    \left(\frac{7}{6}\right)^2 = \frac{49}{36}

    \left(\frac{1}{6}\right)^2 = \frac{1}{36}

    \left(\frac{19}{6}\right)^2 = \frac{361}{36}

    \left(-\frac{7}{6}\right)^2 = \frac{49}{36}

    \left(\frac{13}{6}\right)^2 = \frac{169}{36}

    4. Add the squares:

    625 + 49 + 1 + 361 + 49 + 169 = 1254

    So, we have: \frac{1254}{36}

    5. Now we divide by the number of values:

    \frac{\frac{1254}{36}}{6} = \frac{1254}{216}

    6. Now we take the positive square root of what we have so far:

    \sqrt{\frac{1254}{216}} = 2.4095

    And there you go.

    A formula would be:

    \sigma = \sqrt{\frac{1}{N}\sum^N_{i=1} (x_i - \bar{x})^2}

    Where:

    \sigma = \text{Standard Deviation}

    N = \text{Number of data points}

    x_i = \text{i-th data point}

    \bar{x} = \text{Arithmetic Mean of data points}
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  3. #3
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    Quote Originally Posted by Aryth View Post
    I'll do the Standard Deviation for Item 2:

    1: Find arithmetic mean:

    \frac{(1 + 6 + 5 + 8 + 4 + 7)}{6} = \frac{31}{6} = 5.1666667

    2. Find the deviation of each number from the mean:

    1 - 5.1666667 = -4.1666667 = -\frac{25}{6}

    6 - 5.1666667 = 1.1666667 = \frac{7}{6}

    5 - 5.1666667 = 0.1666667 = \frac{1}{6}

    8 - 5.1666667 = 3.1666667 = \frac{19}{6}

    4 - 5.1666667 = -1.1666667 = -\frac{7}{6}

    7 - 5.1666667 = 2.1666667 = \frac{13}{6}

    3. Square each Deviation:

    \left(-\frac{25}{6}\right)^2 = \frac{625}{36}

    \left(\frac{7}{6}\right)^2 = \frac{49}{36}

    \left(\frac{1}{6}\right)^2 = \frac{1}{36}

    \left(\frac{19}{6}\right)^2 = \frac{361}{36}

    \left(-\frac{7}{6}\right)^2 = \frac{49}{36}

    \left(\frac{13}{6}\right)^2 = \frac{169}{36}

    4. Add the squares:

    625 + 49 + 1 + 361 + 49 + 169 = 1254

    So, we have: \frac{1254}{36}

    5. Now we divide by the number of values:

    \frac{\frac{1254}{36}}{6} = \frac{1254}{216}

    6. Now we take the positive square root of what we have so far:

    \sqrt{\frac{1254}{216}} = 2.4095

    And there you go.

    A formula would be:

    \sigma = \sqrt{\frac{1}{N}\sum^N_{i=1} (x_i - \bar{x})^2}

    Where:

    \sigma = \text{Standard Deviation}

    N = \text{Number of data points}

    x_i = \text{i-th data point}

    \bar{x} = \text{Arithmetic Mean of data points}
    Thanks! I think I've figured it out now.
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  4. #4
    Lee
    Lee is offline
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    st deviation query

    Can you explain how you got top numbers in step 2......25/6, 1/6 etc?

    Thanks
    Lee
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