How do you measure distribution?
Question
Explain or give name of the methods used to measure distribution
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Statistics
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Answers ( 11 )
There are two ways to do that:
1. Descriptive Statistics,
2. Graphical Representation.
In first we can calculate, mean, median, mode, Koutosis, Skewness, Variance, and other descriptive statistics for the distribution.
Second, we can plot the Histograms (with normal line/ trend line), Boxplots, n-grams, Q-Q plots to see how our distribution looks like. is it bi-modular or uni-modular, we can do it by comparing with the normal bell-shaped curve.
You can measure distribution through
mean – gives the average value
median – value at the 50th percentile
mode – value occurring maximum no of times
range – max value – min value
inter-quartile range – 25th to 75th percentile
variance – to get the measure of spread
standard deviation – it also measures the spread but is more standardised than variance
so as to easily compare with other variables.
box plots – give you the max,min,75th,50th and 25th percentile values.
Distributions are mainly measured by their parameters or by plotting graphs. Parameters are more viable for measuring any distribution
Below gives the distribution name with their parameters to measure them
Distribution Parameter 1 Parameter 2 Parameter 3
Chi-square Degrees of freedom
Normal Mean Standard deviation
3-ParameterGamma Shape Scale Threshold
The measurement of Distribution is done with the five number summary.
i.e; Min, Q1,Median,Q2,Max
#Minimum value(Min)
#Maximum Value(Max)
#Q1= first quartile -which means that the
bottom 25 % of data points in the set are found in Q1
#Q3= third quartile- means 75% of data points in the set are found in the Q3
# Median= Middle value which separates the higher half from the lower half.
Some other interesting measures are :
Mean= Average or simply called balancing point
Mode= it gives the value which occurs the most
Range= the difference between the largest value and the smallest value
Interquartile range(IQR)= the difference between the median of the upper
half and the median of the lower half
We can basically measure distribution by plotting graphs.
Boxplot, Q-Q graph, pairplot, histograms
and we can also measure distribution by:
Mean
Median
Mode
Variance
Standard Deviation
Quantiles
The measure of dispersion is categorized as:
(i) An absolute measure of dispersion:
The measures which express the scattering of observation in terms of distances i.e., range, quartile deviation.
The measure which expresses the variations in terms of the average of deviations of observations like mean deviation and standard deviation.
(ii) A relative measure of dispersion:
We use a relative measure of dispersion for comparing distributions of two or more data set and for unit free comparison. They are the coefficient of range, the coefficient of mean deviation, the coefficient of quartile deviation, the coefficient of variation, and the coefficient of standard deviation.
Range: It is the difference between two extreme observations of the data set.
Quartile Deviation: The quartiles divide a data set into quarters. The first quartile, (Q1) is the middle number between the smallest number and the median of the data. The second quartile, (Q2) is the median of the data set. The third quartile, (Q3) is the middle number between the median and the largest number.
Mean Deviation: Mean deviation is the arithmetic mean of the absolute deviations of the observations from a measure of central tendency.
Standard Deviation: A standard deviation is the positive square root of the arithmetic mean of the squares of the deviations of the given values from their arithmetic mean.
The square of the standard deviation is the variance. It is also a measure of dispersion.
Coefficient of Dispersion: Whenever we want to compare the variability of the two series which differ widely in their averages. Also, when the unit of measurement is different.
Coefficient of Variation:100 times the coefficient of dispersion based on standard deviation is the coefficient of variation (C.V.).
We can measure distribution through
1) mean – gives the average value
2) median – value at the 50th percentile
3) mode – value occurring maximum no of times
4) range – max value – min value
5) inter-quartile range – 25th to 75th percentile
6) variance – to get the measure of spread
7) standard deviation – it also measures the spread but is more standardized than the variance
so as to easily compare with other variables.
Distribution =dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed.Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range.
Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.
We can measure distribution through
1) mean – gives the average value
2) median – value at the 50th percentile
3) mode – value occurring maximum no of times
4) range – max value – min value
5) inter-quartile range – 25th to 75th percentile
6) variance – to get the measure of spread
7) standard deviation – it also measures the spread but is more standardized than the variance
so as to easily compare with other variables.
Distribution tells us how the data is spread over the entire range.
Measures of Distribution –
Mean, Median, Mode, Range, Quartiles, Variance, Standard Deviation
Also we can come to know about the outliers through Boxplot.
We can measure distribution through
1) mean – gives the average value
2) median –
3) mode – value occurring maximum no of times
4) range – max value – min value
5) inter-quartile range – 25th to 75th%
6) variance – to get the measure of spread
7) standard deviation – it also measures the spread but is more standardized than the variance.