Respuesta :
Exact Answer: 2*sqrt(5)
Approximate Answer: 4.4721
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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
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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.
The value of the root mean square which is having sets of 1, 3, 4, 5, and 7 is 4.472.
What is a root mean square (RMS)?
It is the square root of the mean square, which is the arithmetic mean of the squares of the group of values.
The formula of root mean square is given as
[tex]\rm X_{RMS} = \sqrt{\dfrac{x_1^2+x_2^2+x_3^2+....+x_n^2}{N}}[/tex]
N be the total number of observations.
The sets 1, 3, 4, 5, and 7.
Then the root mean square will be
[tex]\rm X_{RMS} = \sqrt{\dfrac{1^2+3^2+4^2+5^2+7^2}{5}}\\\\X_{RMS} = \sqrt{\dfrac{1+9+16+25+49}{5}}\\\\X_{RMS} = \sqrt{\dfrac{100}{5}}\\\\X_{RMS} = \sqrt{20}\\\\X_{RMS} = 4.472[/tex]
More about the root mean square link is given below.
https://brainly.com/question/7213287
