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How do sample size confidence level and standard deviation affect the margin of error?
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A score set has a mean of 53 and a standard deviation of 5.6 If each score was multiplied by 0.9 and then had 7 added state the new standard deviation?
Standard deviation is the spread of the data. If each score has 7 added, this would not affect the spread of the data - it would be just as evenly spaced or clumped up, but 7 greater. The only thing that would affect the spread is multiplying every data point by 0.9. This makes distances between the data points 0.9 times as big, and thus makes the standard deviation 0.9 times as big. The standard deviation was 5.6, and so now is 5.6x0.9 = 5.04
How is expected rate of return calculated from average rate of return on investment and standard deviation?
The expected rate of return is simply the average rate of return. The standard deviation does not directly affect the expected rate of return, only the reliability of that estimate.
What are outliers and how do they affect data?
Outliers are observations that are unusually large or unusually small. There is no universally agreed definition but values smaller than Q1 - 1.5*IQR or larger than Q3 + 1.5IQR are normally considered outliers. Q1 and Q3 are the lower and upper quartiles and Q3-Q1 is the inter quartile range, IQR. Outliers distort the mean but cannot affect the median. If it distorts the median, then most of the data are rubbish and the data set should be examined thoroughly. Outliers will distort measures of dispersion, and higher moments, such as the variance, standard deviation, skewness, kurtosis etc but again, will not affect the IQR except in very extreme conditions.
How intelligent is an IQ of 145?
It depends on what the standard deviation for that particular scale is. The most well-known scales have standard deviations of 15. In that case, 145 is three standard deviations above the average. People with this score are considered borderline geniuses. You can expect a well-educated student who has this IQ to be about six, maybe seven years ahead of his classmates. Someone with this IQ is incredibly intelligent and creative. Creativity, in this sense, is not artistic talent. It is the ability to solve logical problems using previously unknown methods. For example, someone who creates a new way to solve sudoku problems is intelligent, not someone who learns how to use them. One in 741 people reach the fourth standard deviation (an IQ of 145 or above in this case). IQ does not measure academic skill. It measures academic potential. The IQ test on tickle.com should be thought of as an aptitude test. Tests that measure actual IQ have questions similar to those on iqtest.dk. Even the WISC and WAIS IQ tests have questions which should only be put in aptitude tests. Remember that no matter which test it is, an online test is invalid. Even if it's a well made, properly calibrated test, your surroundings can affect your score.
