Statistics calculator (100)

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Calculate the mean, median, mode, standard deviation and many more relevant statistical indices of a one-dimension data set.
This tool allows you to calculate a number of statistical coefficients and indices that describe and summarize a one-dimension data set. The data can either represent an entire population or a sample of such population.

In particular, the calculator measures the following coefficients:

  • Central Tendency
    • Mean: Arithmetic mean of the values . It is calculated as the sum of all the data values divided by the size of the sample.
    • Median: The median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half. For a data set, it may be thought of as the “middle” value. For example, in the data set {1, 3, 3, 6, 7, 8, 9}, the median is 6, the fourth largest, and also the fourth smallest, number in the sample.
    • Mode: The mode of a set of data values is the value that appears most often. The mode is not necessarily unique to a given discrete distribution, since the probability mass function may take the same maximum value at several points.
  • Dispersion 1
    • Minimum: The sample minimum, also called the smallest observation, is the value of the smallest element of a sample. It is the last order statistics.
    • Maximum: The sample maximum also called the largest observation, is the value of the greatest element of a sample. It is the first order statistics.
    • Range: In statistics, the range of a set of data is the difference between the largest and smallest values. However, in descriptive statistics, this concept of range has a more complex meaning. The range is the size of the smallest interval which contains all the data and provides an indication of statistical dispersion. It is measured in the same units as the data. Since it only depends on two of the observations, it is most useful in representing the dispersion of small data sets.
    • Mid-range: The mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set, defined as: (X(n)-X(1))/2.
    • Quartile 1: Quartiles are values that divide a set of ordered data into four equal parts. The first quartile, lower quartile or Q1 is the value that divides the 25% lowest values of the sample from the 75% highest values.
    • Quartile 2: Quartiles are values that divide a set of ordered data into four equal parts. The second quartile or Q2 is the value that divides the 25% the data set into two equal halves. It is the median of the data.
    • Quartile 3: Quartiles are values that divide a set of ordered data into four equal parts. The third quartile, upper quartile or Q3 is the value that divides the 75% lowest values of the sample from the 25% highest values.
    • Interquartile Range: The interquartile range (IQR), midspread, middle 50% or H-spread, is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles.
  • Dispersion 2
    • Variance (P): Variance measures how far a set of numbers are spread out from their average value. Population variance or, simply, variance, is used when every object in the population is counted. It is computed as the average of the squared differences between data values and the mean. If the population is too large and only a sample is considered, sample variance must be used.
    • Variance (S): Variance measures how far a set of numbers are spread out from their average value. Sample variance is used when only a sample of the population is considered in the calculations. Sample variance is computed multiplying the population variance by a correction factor (N/(N-1)) that eliminates bias in unbiased estimation or the population variance. Population variance is used when every object in the population is counted. It is computed as the average of the squared differences between data values and the mean.
    • Standard Deviation (P): The standard deviation is the square root of the variance. It measures the dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values. The population standard deviation is used when every object in the population is counted. If only a sample is considered the sample standard deviation must be used.
    • Standard Deviation (S): The standard deviation is the square root of the variance. It measures the dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values. The sample standard deviation is used when just a sample from the population is counted. If every object in the population is considered the population standard deviation must be used.
    • Coefficient of Variation: Coefficient of variation (population) or relative standard deviation, is a measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage, and is defined as the ratio of the population standard deviation to the mean.
    • Mean Deviation: The mean deviation, mean absolute deviation or average absolute deviation is the mean of the data's absolute deviations around the data's mean. It is a summary statistic of statistical dispersion or variability.
    • Standard Error (Mean): The standard error equals the sample standard deviation divided by the square root of the sample size. It is a measure of the dispersion of sample means around the population mean, when repeated sampling and recording of the means are made.
  • Shape
    • Skewness: Skewness describes the shape of a frequency distribution curve. Skewness measures the asymmetry of the data values about its mean.It is computed as the sum of the cubed differencesbetween data values and the mean, divided by the size minus 1 times the cubed standard deviation; The skewness value can be positive, negative or undefined. If the distribution has a negative skew, the left tail is longer, and the mass of the distribution is concentrated on the right of the figure. Conversely, if the distribution has a positive skew, the right tail is longer, and the mass of the distribution is concentrated on the left of the figure.
    • Kurtosis: Kurtosis describes the shape of frequency distribution curve. Kurtosis measures the length and thickness of its tails. Higher values indicate longer and fatter tails; lower values indicate shorter and thinner tails.
  • Miscellaneous
    • Size: Count of the individual samples or observations.
    • Sum: Sum of all the values of the data set.
    • Sum of Squares: Sum of the square of the values of the data set.
    • Mean of Squares: Mean of the square of the data values. Its computed dividing the sum of the square of the values by the size of the sample.

Instructions

  • Enter data values separated by commas.
  • Select an statistics coefficient.
  • A description of the coefficient and its value will appear below.
  • Click “Details” if you want to see the whole list of coefficients.

Important

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This statistics calculator allows you to enter a maximum of 100 values. Please, use our Statistics calculator (1000)  if you need to enter up to 1000 values.