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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.
Does outlier affect standard deviation?
Yes.
How do sample size confidence level and standard deviation affect the margin of error?
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If each score in a set of scores were increased by 6 points how would this affect the mean and the standard deviation?
This would increase the mean by 6 points but would not change the standard deviation.
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.
How would the mean and standard deviation change if the largest data in each set were removed?
Yes. The standard deviation and mean would be less. How much less would depend on the sample size, the distribution that the sample was taken from (parent distribution) and the parameters of the parent distribution. The affect on the sampling distribution of the mean and standard deviation could easily be identified by Monte Carlo simulation.
What are the factors that affecting the quality of data?
Trends, covariance, and correlation are the big ones. Statistical significance, unit roots, heteroskedasticity, and format and source of the data would affect quality too.
Why is statistical significance not necessarily of practical importance to a business decision?
Some data in statistics can affect numbers, which will skew the data. When this happens managers should make business decisions that ignore the stats.
If two distributions have exactly the same mean and standard deviation must their histograms have the same shape If they have the same five-number summary must their histograms have the same shape?
No, and no. Think about two skewed distributions that are mirrored across the mean so that one is right and one is left. they have the same mean and standard deviation, but are opposite. Also, the 5 number summary does not affect a histogram
How does sample size affect t score?
The estimated standard deviation goes down as the sample size increases. Also, the degrees of freedom increase and, as they increase, the t-distribution gets closer to the Normal distribution.
How does a stroke affect tongue deviation?
A stroke can affect tongue deviation by causing weakness or paralysis in the muscles that control the tongue. This can lead to difficulty in moving the tongue properly, resulting in deviations or abnormal movements when speaking or swallowing.
What is the difference between error propagation and standard deviation in the context of data analysis?
Error propagation refers to the way errors in measurements or calculations can affect the final result in a data analysis process. It involves quantifying how uncertainties in the input data contribute to the uncertainty in the final result. On the other hand, standard deviation is a measure of the dispersion or spread of data points around the mean. It provides information about the variability or consistency of the data set, but it does not directly account for how errors in individual data points may affect the final analysis result.
