Quadratic Mean The quadratic mean (or root mean square , or R.M.S. ) is used in physical applications, such as power distribution systems. The quadratic mean of a set of values is obtained by squaring each value, adding those squares, dividing the sum by the number of values n , and then taking the square root of that result, as indicated below: Quadratic mean = ∑ x 2 n Find the R.M.S. of these voltages measured from household current: 0, 60,110, −110, −60.0. How does the result compare to the mean?
Quadratic Mean The quadratic mean (or root mean square , or R.M.S. ) is used in physical applications, such as power distribution systems. The quadratic mean of a set of values is obtained by squaring each value, adding those squares, dividing the sum by the number of values n , and then taking the square root of that result, as indicated below: Quadratic mean = ∑ x 2 n Find the R.M.S. of these voltages measured from household current: 0, 60,110, −110, −60.0. How does the result compare to the mean?
Solution Summary: The author calculates the root mean square (R.M.S) and the mean for the voltages measured from household current.
Quadratic Mean The quadratic mean (or root mean square, or R.M.S.) is used in physical applications, such as power distribution systems. The quadratic mean of a set of values is obtained by squaring each value, adding those squares, dividing the sum by the number of values n, and then taking the square root of that result, as indicated below:
Quadratic mean =
∑
x
2
n
Find the R.M.S. of these voltages measured from household current: 0, 60,110, −110, −60.0. How does the result compare to the mean?
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
The accompanying table shows the height (in inches) of 8 high school girls and their scores on an IQ test. Complete parts (a) through (d) below.
Data Table:
Height, x IQ score, y61 10359 9866 10166 10758 9264 10464 11556 122
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the table of critical values for the Pearson correlation coefficient.
n alpha=0.05 alpha=0.014 0.950 0.9905 0.878 0.9596 0.811 0.9177 0.754 0.8758 0.707 0.8349 0.666 0.79810 0.632 0.76511 0.602 0.73512 0.576 0.70813 0.553 0.68414 0.532 0.66115 0.514 0.64116 0.497 0.62317 0.482 0.60618 0.468 0.59019 0.456 0.57520 0.444 0.56121 0.433 0.54922 0.423 0.53723 0.413 0.52624 0.404 0.51525 0.396 0.50526 0.388 0.49627 0.381 0.48728 0.374 0.47929 0.367 0.47130 0.361 0.46335 0.334 0.43040 0.312 0.40345 0.294 0.38050 0.279 0.36155 0.266 0.34560…
The ones in the parenthesis will say the concept of rounding off.
For example: (in 1 decimal place) means rounding off your answer in 1 decimal place. Provide solution if possible
An administrative assistant for the athletics department at a local university is moni-
toring the GPAs for eight members of the women's volleyball team. He enters the
GPAs into the database but accidentally misplaces the decimal point in the last entry.
2.8 3.0 3.0 3.3 2.4 3.4 3.0 21
Use a dotplot to describe the data and uncover the assistant's mistake.
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