mode and skew
To obtain a much better, simpler, and more practical understanding of the data distribution.
The answer will depend on what you mean by "solve". Find the mean, median, mode, variance, standard error, standard deviation, quartiles, deciles, percentiles, cumulative distribution, goodness of fit to some distribution etc. The question needs to be a bit more specific than "solve".
characteristics of mean
'Mean', 'mode', 'median' and 'standard deviation' are all quantities used in statistics. Each one is an attempt to use a single number to describe the essential nature and character of a bunch of numbers.
The mean, median, and mode of a normal distribution are equal; in this case, 22. The standard deviation has no bearing on this question.
mode and skew
To obtain a much better, simpler, and more practical understanding of the data distribution.
For data sets having a normal distribution, the following properties depend on the mean and the standard deviation. This is known as the Empirical rule. About 68% of all values fall within 1 standard deviation of the mean About 95% of all values fall within 2 standard deviation of the mean About 99.7% of all values fall within 3 standard deviation of the mean. So given any value and given the mean and standard deviation, one can say right away where that value is compared to 60, 95 and 99 percent of the other values. The mean of the any distribution is a measure of centrality, but in case of the normal distribution, it is equal to the mode and median of the distribtion. The standard deviation is a measure of data dispersion or variability. In the case of the normal distribution, the mean and the standard deviation are the two parameters of the distribution, therefore they completely define the distribution. See: http://en.wikipedia.org/wiki/Normal_distribution
Mean: 26.33 Median: 29.5 Mode: 10, 35 Standard Deviation: 14.1515 Standard Error: 5.7773
The answer will depend on what you mean by "solve". Find the mean, median, mode, variance, standard error, standard deviation, quartiles, deciles, percentiles, cumulative distribution, goodness of fit to some distribution etc. The question needs to be a bit more specific than "solve".
Yes. By definition. A normal distribution has a bell-shaped density curve described by its mean and standard deviation. The density curve is symmetrical(i.e., an exact reflection of form on opposite sides of a dividing line), and centered about (divided by) its mean, with its spread (width) determined by its standard deviation. Additionally, the mean, median, and mode of the distribution are equal and located at the peak (i.e., height of the curve).
characteristics of mean
Karl Pearson simplified the topic of skewness and gave us some formulas to help. The first is the Pearson mode or first skewness coefficient. It is defined by the (mean-median)/standard deviation. So in this case the Pearson mode is: (8-6)/2 =1 There is also the Pearson Median. This is also called second skewness coefficient. It is defined as 3(mean-median)/standard deviation which in this case is 6/2 =3 hence the distribution is positive skewed
The coefficient of skewness is a measure of asymmetry in a statistical distribution. It indicates whether the data is skewed to the left, right, or is symmetric. The formula for calculating the coefficient of skewness is [(Mean - Mode) / Standard Deviation]. A positive value indicates right skew, a negative value indicates left skew, and a value of zero indicates a symmetric distribution.
'Mean', 'mode', 'median' and 'standard deviation' are all quantities used in statistics. Each one is an attempt to use a single number to describe the essential nature and character of a bunch of numbers.
The mean is the sum of each sample divided by the number of samples.The median is the middle sample in a ranked list of samples, or the mean of the middle two samples if the number of samples is even.The standard deviation is the square root of the sum of the squares of the difference between the mean and each of the samples, such sum then divided by either N or by N-1, before the square root is taken. N is used for population standard deviation, where the mean is known independently of the calculation of the standard deviation. N-1 is used for sample standard deviation, where the mean is calculated along with the standard deviation, and the "-1" compensates for the loss of a "degree of freedom" that such a procedure entails.Not asked, but answered for completeness sake, the mode is the most probable value, and does not necessarily represent the mean such as in an asymmetrically skewed distribution, such as a Poisson distribution.