Find the root mean square of the set 1, 3, 4, 5 and 7

Exact   2*sqrt(5)

Approximate  4.4721

Explanation:

Original set = {1,3,4,5,7}

Square each value to get {1,9,16,25,49}. This is the list of squares.

Add up those squares: 1+9+16+25+49 = 100

Next, divide that over n = 5 which is the number of items in the set

100/n = 100/5 = 20

The value 20 is the mean of the list of squares above.

Lastly, apply the square root to get sqrt(20) = sqrt(4*5) = sqrt(4)*sqrt(5) = 2*sqrt(5)

This approximates to roughly 4.4721

Side note: The term "root mean square" is often abbreviated to "RMS".

If we reversed the order of the three words, then we get "square mean root". In this reversed order, we see that the squaring operation is done first, then the mean next, and finally the square root is done last.

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step-by-step explanation: