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31 March, 13:47

The mean number of hours per day spent on the phone according to a national survey is four hours, with a standard deviation of two hours. If each time was increased by one hour, what would be the new mean and standard deviation

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  1. 31 March, 14:59
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    The new mean would be five hours and the standard deviation would still be two hours.

    Step-by-step explanation:

    Suppose, as an example that you only have four values in the survey x1, x2 x3 and x4 the meaa would be

    (x1+x2+x3+x4) / 4

    If you add one to each number then the mean would be:

    ((x1+1) + (x2+1) + (x3+1) + (x4+1)) / 4 = (x1+x2+x3+x4+4) / 4 = (x1+x2+x3+x4) / 4 + (4/4) = (x1+x2+x3+x4/4) + 1 = original mean + 1

    As you see the mean value, no matter the values you add, is the original plus one.

    The standard deviation measures the spread or dispersion of your values around the mean. If you add one to all values, all values are equally far from the mean as the original case. For example, if you have two values, 2 and 6 the means is is 4. 2 is two units far from four as well as 6. If I add one to the values, I have 3 and 7 and the mean is 5. As the mean has also changed the distance of the new numbers keeps being two units far. Adding the same number to all observations will never change standard deviation.
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