Standard deviation of 0 can only be attained if all observations are identical. That is, the variable in question has just one possible value so statistical considerations are irrelevant.
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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
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.
Zero is not considered significant when it serves as a placeholder in a numerical value, such as in 100 or 0.004, where it does not affect the precision of the measurement. It also doesn't hold significance in mathematical operations that result in an undefined or irrelevant outcome, such as division by zero. Additionally, in certain contexts, such as statistical analysis, zero may represent a lack of effect or absence of a value, which can also render it non-significant.
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.
Yes.
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This would increase the mean by 6 points but would not change the 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
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.
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.
Trends, covariance, and correlation are the big ones. Statistical significance, unit roots, heteroskedasticity, and format and source of the data would affect quality too.
Some data in statistics can affect numbers, which will skew the data. When this happens managers should make business decisions that ignore the stats.
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
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.
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.
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.