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Is the standard deviation best thought of as the distance from the mean?
No. A small standard deviation with a large mean will yield points further from the mean than a large standard deviation of a small mean. Standard deviation is best thought of as spread or dispersion.
Is the line of best fit the same as linear regression?
Linear Regression is a method to generate a "Line of Best fit" yes you can use it, but it depends on the data as to accuracy, standard deviation, etc. there are other types of regression like polynomial regression.
Merits and demerits of quartile deviation?
Merits· It can be easily calculated and simply understood.· It does not involve much mathematical difficulties.· As it takes middle 50% terms hence it is a measure better than Range and percentile Range.· It is not affected by extreme terms as 25% of upper and 25% of lower terms are left out.· Quartile Deviation also provides a short cut method to calculate Standard Deviation using the formula 6 Q.D. = 5 M.D. = 4 S.D.· In case we are to deal with the centre half of a series this is the best measure to use.Demerits or Limitations· As Q1 and Q3 are both positional measures hence are not capable of further algebraic treatment.· Calculation are much more, but the result obtained is not of much importance.· It is too much affected by fluctuations of samples.· 50% terms play no role; first and last 25% items ignored may not give reliable result.· If the values are irregular, then result is affected badly.· We can't call it a measure of dispersion as it does not show the scatter-ness around any average.· The value of quartile may be same for two or more series or Q.D. is not affected by the distribution of terms between Q1 and Q3 or outside these positions.So going through the merits and demerits, we conclude that Quartile Deviation cannot be relied on blindly. In the case of distributions with high degree of variation, quartile deviation has less reliability.
Mutual funds performance is best measured by?
There are a few key ways to measure the performance of mutual funds: Total return - The total return of a mutual fund includes dividends, capital gains distributions, and the change in net asset value (NAV) per share over a given time period. This provides the most complete picture of a fund's overall performance. Sharpe ratio - The Sharpe ratio measures a fund's return relative to the amount of risk taken to generate that return. It provides insight into the fund's risk-adjusted returns. The higher the Sharpe ratio, the better the risk-adjusted returns. Standard deviation - Standard deviation measures the volatility or variability of a fund's returns over time. A higher standard deviation indicates wider fluctuations in returns from year to year. This helps gauge the fund's risk levels. Benchmark comparisons - Comparing a mutual fund's returns to an appropriate benchmark index (e.g. S&P 500 index for large-cap US equity funds) provides perspective on how well the fund performed versus the broader market. Outperforming the benchmark generally indicates good fund management. In summary, total return, risk-adjusted return metrics like Sharpe ratio, volatility measures like standard deviation, and benchmark comparisons together provide the most comprehensive view of a mutual fund's overall performance. These metrics taken together can determine if a fund successfully met its investment objective over a period.
What is the relationship between confidence interval and standard deviation?
Short answer, complex. I presume you're in a basic stats class so your dealing with something like a normal distribution however (or something else very standard). You can think of it this way... A confidence interval re-scales margin of likely error into a range. This allows you to say something along the lines, "I can say with 95% confidence that the mean/variance/whatever lies within whatever and whatever" because you're taking into account the likely error in your prediction (as long as the distribution is what you think it is and all stats are what you think they are). This is because, if you know all of the things I listed with absolute certainty, you are able to accurately predict how erroneous your prediction will be. It's because central limit theory allow you to assume statistically relevance of the sample, even given an infinite population of data. The main idea of a confidence interval is to create and interval which is likely to include a population parameter within that interval. Sample data is the source of the confidence interval. You will use your best point estimate which may be the sample mean or the sample proportion, depending on what the problems asks for. Then, you add or subtract the margin of error to get the actual interval. To compute the margin of error, you will always use or calculate a standard deviation. An example is the confidence interval for the mean. The best point estimate for the population mean is the sample mean according to the central limit theorem. So you add and subtract the margin of error from that. Now the margin of error in the case of confidence intervals for the mean is za/2 x Sigma/ Square root of n where a is 1- confidence level. For example, confidence level is 95%, a=1-.95=.05 and a/2 is .025. So we use the z score the corresponds to .025 in each tail of the standard normal distribution. This will be. z=1.96. So if Sigma is the population standard deviation, than Sigma/square root of n is called the standard error of the mean. It is the standard deviation of the sampling distribution of all the means for every possible sample of size n take from your population ( Central limit theorem again). So our confidence interval is the sample mean + or - 1.96 ( Population Standard deviation/ square root of sample size. If we don't know the population standard deviation, we use the sample one but then we must use a t distribution instead of a z one. So we replace the z score with an appropriate t score. In the case of confidence interval for a proportion, we compute and use the standard deviation of the distribution of all the proportions. Once again, the central limit theorem tells us to do this. I will post a link for that theorem. It is the key to really understanding what is going on here!
Why is standard deviation called the best of all measures of dispersion?
standard deviation is the best measure of dispersion because.. a)It measure the absolute dispersion b)It is most frequentlyused as prossesses almost all the the qualities that a good measure of variation have. c)It is beased on all observation. d)It is rigidly defined. e)It is capable of further algebraic treatment. f)It is least affected by the fluctuation of sampling.
Is the standard deviation best thought of as the distance from the mean?
No. A small standard deviation with a large mean will yield points further from the mean than a large standard deviation of a small mean. Standard deviation is best thought of as spread or dispersion.
What does the sample standard deviation best estimate?
The standard deviation of the population. the standard deviation of the population.
What is best measure of risk for an asset held in isolation and which is the best measure for an asset held in a diversified portfolio?
Standard deviation; correlation coefficient
How standard deviation and Mean deviation differ from each other?
There is 1) standard deviation, 2) mean deviation and 3) mean absolute deviation. The standard deviation is calculated most of the time. If our objective is to estimate the variance of the overall population from a representative random sample, then it has been shown theoretically that the standard deviation is the best estimate (most efficient). The mean deviation is calculated by first calculating the mean of the data and then calculating the deviation (value - mean) for each value. If we then sum these deviations, we calculate the mean deviation which will always be zero. So this statistic has little value. The individual deviations may however be of interest. See related link. To obtain the means absolute deviation (MAD), we sum the absolute value of the individual deviations. We will obtain a value that is similar to the standard deviation, a measure of dispersal of the data values. The MAD may be transformed to a standard deviation, if the distribution is known. The MAD has been shown to be less efficient in estimating the standard deviation, but a more robust estimator (not as influenced by erroneous data) as the standard deviation. See related link. Most of the time we use the standard deviation to provide the best estimate of the variance of the population.
What is the best measure of variability?
The best measure of variability depends on the specific characteristics of the data. Common measures include the range, standard deviation, and variance. The choice of measure should be made based on the distribution of the data and the research question being addressed.
What is the angle of minimum deviation in a diffraction experiment?
The angle of minimum deviation in a diffraction experiment is the angle at which the diffracted light rays are the most spread out, resulting in the best separation of the different colors. It is typically smaller than the angle of the first diffraction minimum to achieve maximum dispersion.
What is the best measure of a nation's standard of living?
GDP per capita
What is the best standard unit to measure a persons height?
feet and inches
What are the best statistics to use for data that is normally distributed?
The mean and standard deviation. If the data really are normally distributed, all other statistics are redundant.
What is the best unit of measure to measure your bookshelf?
The best unit of measure to measure a bookshelf would be inches or centimeters, depending on the standard unit of measurement you prefer. These units provide a precise representation of the bookshelf's dimensions.
'What is the best formula for detection limit?
The best formula for detection limit is usually the limit of detection (LOD) or the limit of quantification (LOQ). These are commonly calculated using the signal-to-noise ratio method, where the limit of detection is three times the standard deviation of the blank signal divided by the slope of the calibration curve, and the limit of quantification is ten times the standard deviation of the blank signal divided by the slope of the calibration curve.
