A population standard deviation of 1 indicates that the data points in the population tend to deviate from the mean by an average of 1 unit. It reflects the degree of variation or dispersion within the dataset; a smaller standard deviation would suggest that the data points are closer to the mean, while a larger one would indicate more spread out values. In practical terms, if the population's values are measured in a certain unit, most of the data will fall within one unit above or below the mean.
In a normal distribution, approximately 68% of the population falls within one standard deviation of the mean, and about 95% falls within two standard deviations. Therefore, to find the percentage of the population between one standard deviation below the mean and two standard deviations above the mean, you would calculate 95% (within two standard deviations) minus 34% (the portion below one standard deviation), resulting in approximately 61% of the population.
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.
For the numbers 4, 43, 63, 84, 54, 84 and 1, the standard deviation is 34.20943896 and the mean is 47.57142857.
standard normal
with mean of and standard deviation of 1.
Assuming a normal distribution 68 % of the data samples will be with 1 standard deviation of the mean.
=stdev(...) will return the N-1 weighted sample standard deviation. =stdevp(...) will return the N weighted population standard deviation.
Mean 0, standard deviation 1.
Mean = 0 Standard Deviation = 1
16.5 is 1 standard deviation from the mean. If you add the mean of 14 to the 1 standard deviation of 2.5, the result is 16.5.
Standard deviation is a measure of variation from the mean of a data set. 1 standard deviation from the mean (which is usually + and - from mean) contains 68% of the data.
1. mu (population mean) 2. sigma (population standard deviation)
If the population standard deviation is sigma, then the estimate for the sample standard error for a sample of size n, is s = sigma*sqrt[n/(n-1)]
400
a is true.
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.
No.