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How can I calculate the standard deviation of a data set?

The formula for the variance of a data set can be easily remembered by this catchy phrase: 'The mean of the squares minus the square of the mean'. The standard deviation is equal to the square root of the va...
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Answered by Robin M. • Maths tutor
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Prove by mathematical induction that 11^n-6 is divisible by 5 for all natural numbers n

First I would do the base case (the first value):Test n=1,11 1 -6=5. 5 is divisible by 5 therefore true for n=1. Now we assume true for n=k,11 k -6 is divisible by 5.Next we test n=k+1,11 k+1 -6We can rearra...
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∫ x^3 *ln(2x) (from 2->1) can be written in the form pln 2 + q, where p and q are rational numbers. Find p and q.

Firstly I would think about how I could integrate this. In this case you would need integrate by parts. I use LATE to decide which value is u and v' which stands for Log,Algebra,Trig,Exp. Which ever one appe...
Answered by • Maths tutor
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Use differentiation to show the function f(x)=2x^3–12x^2+25x–11 is an increasing function for all values of x

Firstly, I would remember what differentiation shows - which is the rate of change of a function. I would think about how I could use this to show it's always increasing. Now the first derivative would show ...
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Inwiefern ist der Kölner Dom ein bedeutendes Bauwerk?

Der Kölner Dom ist die größte gotische Kirche in Europa und hat die größte Kirchfassade der Welt. Aber der Dom ist nicht nur groß, sondern auch besonders alt. Sein Bau wurde 1248 begonnen und erst 1880 volle...
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Answered by Fiona P. • German tutor
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