Note: The average and standard deviation are expressed as percentages, while the variance is a decimal number.
The standard deviation is a measure of the spread of a set of data, and the relative standard deviation (also known as the coefficient of variation) is the ratio of the standard deviation to the mean, expressed as a percentage.
The relative standard deviation (RSD) is often times more convenient. It is expressed in percent and is obtained by multiplying the standard deviation by 100 and dividing this product by the average.
The 68-95-99 rule
It says: 68% of the population is within 1 standard deviation of the mean. 95% of the population is within 2 standard deviation of the mean. 99.7% of the population is within 3 standard deviation of the mean.
Answer and Explanation: A sample with a standard deviation equal to 5 indicates that, on average, the distance between each data point in an entire dataset is different from the mean of the dataset by a value of 5.
The standard deviation of the normal distribution is about 10, provided that the mean of the data is approximately 100. The normal distribution can take on any value for the mean and the standard deviation, provided that the data appear to be normally distributed.
So as a purely internal measure of High / Low Std deviation I chose to say if the SD was less than 10% of the range then its low, greater than 10% of the range then high.
In normally distributed data, about 34% of the values lie between the mean and one standard deviation below the mean, and 34% between the mean and one standard deviation above the mean. In addition, 13.5% of the values lie between the first and second standard deviations above the mean.
Around 95% of values are within 2 standard deviations of the mean. Around 99.7% of values are within 3 standard deviations of the mean.
Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean. In any distribution, about 95% of values will be within 2 standard deviations of the mean.
Statisticians have determined that values no greater than plus or minus 2 SD represent measurements that are are closer to the true value than those that fall in the area greater than ± 2SD. Thus, most QC programs require that corrective action be initiated for data points routinely outside of the ±2SD range.
%RSD (relative standard deviation) is a statistical measurement that describes the spread of data with respect to the mean and the result is expressed as a percentage. The %RSD function is popular with non-statisticians as the interpretation is based on a percent result and not some abstract value.
95% of the population is within 2 standard deviations of the mean. 99% of the population is within 2 1/2 standard deviations of the mean. 99.7% of the population is within 3 standard deviations of the mean. 99.9% of the population is within 4 standard deviations of the mean.
Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out. A standard deviation close to zero indicates that data points are close to the mean, whereas a high or low standard deviation indicates data points are respectively above or below the mean.
Three standard deviations include all the numbers for 99.7% of the sample population being studied. This is true if the distribution is normal (bell-shaped).
Step 3: Calculate the variance of the returns using the VAR function. Step 4: Calculate standard deviation of the returns using the STDEV function. Note: The average and standard deviation are expressed as percentages, while the variance is a decimal number.
To capture the central 90%, we must go out 1.645 standard deviations on either side of the calculated sample mean.
Since this CV value is greater than 1, it tells us that the standard deviation of the data values are quite high.
Let's suppose the average (mean) income in the sample is $100,000, and the (sample) standard deviation is $10,000. The standard deviation of $10,000 gives us an indication of how much, on average, incomes deviate from the mean of $100,000. A standard error is a measure of how precise an estimate is.
Given: The mean of a distribution is 10 and the standard deviation is 5. ∴ The value of variance coefficient is 50%.
On the other hand, if the data set has a smaller SD (e.g., SD = 0.3), you can infer that the data points are closer to the mean.