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What else can I help you with?
What is the definition of Standard deviation of a single measurement?
The standard deviation of a single observation is not defined. With a single observation, the mean of the observation(s) would be the same as the value of the observation itself. By definition, therefore, the deviation (difference between observation and mean) would always be zero. Rather a pointless exercise!
When is a t-test performed instead of a z-test?
A t-test is performed instead of a z-test when the sample size is small (typically n < 30) and the population standard deviation is unknown. The t-test accounts for the increased variability and uncertainty in small samples by using the sample standard deviation rather than the population standard deviation. Additionally, it is often used when the data is approximately normally distributed.
The Sortino Ratio?
I've written before about the Sharpe Ratio, a measure of risk-adjusted returns for an asset or portfolio. The Sharpe ratio functions by dividing the difference between the returns of that asset or portfolio and the risk-free rate of return by the standard deviation of the returns from their mean. So it gives you an idea of the level of risk assumed to earn each marginal unit of return. The problem with using the Sharpe Ratio is that it assumes that all deviations from the mean are risky, and therefore bad. But often those deviations are upward movements. Why should an investment strategy by graded so sharply by the Sharpe Ratio for good performance? In the real world, investors don't usually mind upside deviations from the mean. Why would they? These were the questions on the mind of Frank Sortino when he developed what has been dubbed the Sortino Ratio. The ratio that bears his name is a modification of the Sharpe Ratio that only takes into account negative deviations and counts them as risk. To me, it always made a lot more sense not to include upside volatility from the equation because I rather like to see some upside volatility in my portfolios. With the Sortino Ratio only downside volatility is used as the denominator in the equation. So the way you calculate it is to divide the difference between the expected rate of return and the risk-free rate by the standard deviation of negative asset returns. (It can be a bit tricky the first time you try to do it. The positive deviations are set to values of zero during the standard deviation calculation in order to calculate downside deviation.) By using the Sortino Ratio instead of the Sharpe Ratio you’re not penalizing the investment manager or strategy for any upside volatility in the portfolio. And doesn’t that make a whole lot more sense?
How do you identify random errors?
Random errors can be identified by analyzing the variability in repeated measurements of the same quantity under unchanged conditions. These errors often manifest as fluctuations in data points that do not consistently deviate in the same direction. Statistical methods, such as calculating the standard deviation or using confidence intervals, can help quantify this variability. Additionally, a lack of systematic bias in the data indicates the presence of random errors rather than consistent errors.
What is the deviation angle between geographic and true north in India?
It's rather small in India. In New Delhi, the magnetic compass points 51 minutes east of true north. That error is increasing by about 1 minute per year.
Can The standard deviation of a distribution be a negative value?
No. The standard deviation is not exactly a value but rather how far a score deviates from the mean.
What is the definition of Standard deviation of a single measurement?
The standard deviation of a single observation is not defined. With a single observation, the mean of the observation(s) would be the same as the value of the observation itself. By definition, therefore, the deviation (difference between observation and mean) would always be zero. Rather a pointless exercise!
What statistical measure is not a summary number but rather a comparison between each data value and a single number?
Standard deviation
When is a t-test performed instead of a z-test?
A t-test is performed instead of a z-test when the sample size is small (typically n < 30) and the population standard deviation is unknown. The t-test accounts for the increased variability and uncertainty in small samples by using the sample standard deviation rather than the population standard deviation. Additionally, it is often used when the data is approximately normally distributed.
How do you figure sigma or mu in statistics?
Sigma is used to represent the standard deviation of a dataset. The calculation is rather complex, but if you think of it as the "root of the mean of the squares of the differences" ... rms of differences ... it might make more sense.Enter "standard deviation" on you search engine of choice for details. Wikipedia has a couple of basic examples, and a whole lot more!Mu represents the population mean, or "average" - add all the values and divide by how many.In statistics, you often don't know the population mean, so you take samples and find "x bar", the sample means, then using those to calculate an estimate of the population mean.
How do you calculate salary variance?
I believe you are interested in calculating the variance from a set of data related to salaries. Variance = square of the standard deviation, where: s= square root[sum (xi- mean)2/(n-1)] where mean of the set is the sum of all data divided by the number in the sample. X of i is a single data point (single salary). If instead of a sample of data, you have the entire population of size N, substitute N for n-1 in the above equation. You may find more information on the interpretation of variance, by searching wikipedia under variance and standard deviation. I note that an advantage of using the standard deviation rather than variance, is because the standard deviation will be in the same units as the mean.
Can you do the mean deviation for a grouped data?
Yes, but it rather pointless. The mean deviation for any data set will, by definition, be 0. Grouping may make it slightly different from 0 but this statistic has little, if any, useful properties.
What are requirements for the roman soldiers?
Good health, a rather standard height, and Roman citizenship were all the requirements for the Roman military.Good health, a rather standard height, and Roman citizenship were all the requirements for the Roman military.Good health, a rather standard height, and Roman citizenship were all the requirements for the Roman military.Good health, a rather standard height, and Roman citizenship were all the requirements for the Roman military.Good health, a rather standard height, and Roman citizenship were all the requirements for the Roman military.Good health, a rather standard height, and Roman citizenship were all the requirements for the Roman military.Good health, a rather standard height, and Roman citizenship were all the requirements for the Roman military.Good health, a rather standard height, and Roman citizenship were all the requirements for the Roman military.Good health, a rather standard height, and Roman citizenship were all the requirements for the Roman military.
Is car insurance included in the debt-to-income ratio calculation?
Car insurance is typically not included in the debt-to-income ratio calculation because it is considered a variable expense rather than a fixed debt obligation.
Why is volume of the NaCl solution determined through a mass and density calculation rather than reading the graduated cylinder?
It is not a rule.
What book do Muslims worship from?
Muslims do not worship any book, rather they worship their God, Allah. They do however, believe in the scripture, Qur'an, which is a massive deviation from worship.
Why is the sample deviation divided by n-1in business statistics?
The purpose in computing the sample standard deviation is to estimate the amount of spread in the population from which the samples are drawn. Ideally, therefore, we would compute deviations from the mean of all the items in the population, rather than the deviations from the sample mean. However the population mean is generally unknown, so the sample mean would be used in place. It is a mathematical fact that the deviations around the sample mean tend to be a bit smaller than the deviations around the population mean and by dividing by n-1 rather than n provide the exactly the right amount of correction.
