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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?
Mutual fund performance is best measured by:Growth in the total Assets under managementSteady Growth in the NAV of the fund houseMinimal fund management chargesComparison with the benchmark index and its peers
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!
