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Does variance change when the scale does?

  • 17-02-2015 9:31pm
    #1
    Darkest Horse
    Registered Users, Registered Users 2 Posts: 497 ✭✭


    Hi all. Just changing a sclae from cm to inches but not sure if that changes the standard deviation? Any help appreciated.

    DH


Comments

  • #2
    **Timbuk2**
    Moderators, Education Moderators, Motoring & Transport Moderators Posts: 7,396 Mod ✭✭✭✭**Timbuk2**


    Yes it does change!

    If c is a constant, and if y = c*x, then sd(y) = c * sd(x) and var(y) = c^2 * var(x)

    So for example if the standard deviation of length is 5cm (var = 25 square cms) then converting it to inches would make the standard deviation 5 * 0.394 = 1.97inches (1.97^2 square inches)

    Note the 'unit' of standard deviation is whatever your variables are measured in, and the 'unit' of a variance is the square of the variable units.

    Wiki: Properties of Variances


  • #3
    Darkest Horse
    Registered Users, Registered Users 2 Posts: 497 ✭✭Darkest Horse


    **Timbuk2** wrote: »
    Yes it does change!

    If c is a constant, and if y = c*x, then sd(y) = c * sd(x) and var(y) = c^2 * var(x)

    So for example if the standard deviation of length is 5cm (var = 25 square cms) then converting it to inches would make the standard deviation 5 * 0.394 = 1.97inches (1.97^2 square inches)

    Note the 'unit' of standard deviation is whatever your variables are measured in, and the 'unit' of a variance is the square of the variable units.

    Wiki: Properties of Variances

    Just wanted to drag this up again if it's ok. If, say, a unit of measurement changes from 142 cm to 1.42 m, does that also affect the SD?

    Thanks!

    DH


  • #4
    MathsManiac
    Registered Users, Registered Users 2 Posts: 1,595 ✭✭✭MathsManiac


    If the standard deviation was 142 centimetres, then it will be 1.42 metres when you change units.

    And, since the variance is the square of the standard deviation, in the case above the variance (when working in centimetres) was 20164 cm^2, and when expressed in the new units it will be 2.0164 m^2.


  • #5
    TheSetMiner
    Registered Users, Registered Users 2 Posts: 225 ✭✭TheSetMiner


    Hi. a little of topic but I have a further variance related question. If I have a confidence interval for the variance, can I square root the values of this interval to obtain a confidence interval for the standard deviation?


  • #6
    **Timbuk2**
    Moderators, Education Moderators, Motoring & Transport Moderators Posts: 7,396 Mod ✭✭✭✭**Timbuk2**


    TheSetMiner wrote: »
    Hi. a little of topic but I have a further variance related question. If I have a confidence interval for the variance, can I square root the values of this interval to obtain a confidence interval for the standard deviation?

    Yes


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