Bowley’s Coefficient of Skewness for Ungrouped data Skewness is a measure of symmetry. The meaning of skewness is "lack of symmetry". Skewness gives us an idea about the concentration of higher or lower data values around the central value of the data. For a symmetric distribution, the two quartiles namely $Q_1$ and $Q_3$ are equidistant …
Quartile Deviation for ungrouped data Quartile deviation (QD) is an absolute measure of spread or dispersion based on the quartiles. Quartile deviation is defined as half of the distance between the third quartile $Q_3$ and the first quartile $Q_1$. It is also known as semi-interquartile range. Thus the quartile deviation is given by $QD = …
Harmonic Mean for grouped data Harmonic mean is an important measure of central tendency of the data. Harmonic mean is used for calculating average of ratios. Most commonly used ratios are speed and time, work and time, dividend per share of companies, cost and units materials, etc. Let $(x_i,f_i), i=1,2, \cdots , n$ be given …
Quartile Deviation for grouped data Quartile deviation (QD) is an absolute measure of spread or dispersion based on the quartiles. Quartile deviation is defined as half of the distance between the third quartile $Q_3$ and the first quartile $Q_1$. It is also known as semi-interquartile range. Thus the quartile deviation is given by $QD = …
Five number summary for grouped data A five number summary is a quick and easy way to determine the the center, the spread and outliers (if any) of a data set. Five number summary includes five values, namely, minimum value ($\min$), first quartile ($Q_1$), $\text{median }$ ($Q_2$), third quartile ($Q_3$), maximum value ($\max$). Formula $\min$= …
Kelly’s Coefficient of Skewness for Ungrouped data Kelly’s coefficient of skewness is based on deciles or percentiles of the data. The Bowley’s coefficient of skewness is based on the middle 50 percent of the observations of data set. It means the Bowley’s coefficient of skewness leaves the 25 percent observations in each tail of the …
Kelly’s coefficient of skewness for grouped data Kelly’s coefficient of skewness is based on deciles or percentiles of the data. The Bowley’s coefficient of skewness is based on the middle 50 percent of the observations of data set. It means the Bowley’s coefficient of skewness leaves the 25 percent observations in each tail of the …
Karl Pearson coefficient of skewness for ungrouped data Let $x_i, i=1,2, \cdots , n$ be $n$ observations. The Karl Pearson’s coefficient skewness is given by $S_k =\dfrac{Mean-Mode}{sd}=\dfrac{\overline{x}-Mode}{s_x}$ OR $S_k =\dfrac{3(Mean-Median)}{sd}=\dfrac{3(\overline{x}-M)}{s_x}$ where, $\overline{x}$ is the sample mean of the data, $M$ is the median of the data, $Mode$ is the mode of the data, $s_x$ is …
Coefficient of variation for ungrouped data Coefficient of variation is an absolute measure of variation and is used for the comparison of variability between two or more frequency distribution. Let $x_i, i=1,2, \cdots , n$ be $n$ observations. Coefficient of variation formula is given by $CV =\dfrac{s_x}{\overline{x}}\times 100$ where, $\overline{x} =\dfrac{1}{n}\sum_{i=1}^{n}x_i$ is the sample mean …
Coefficient of variation for grouped data Let $(x_i,f_i), i=1,2, \cdots , n$ be given frequency distribution. Coefficient of variation formula is given by $CV =\dfrac{s_x}{\overline{x}}\times 100$ where, $\overline{x} =\dfrac{1}{N}\sum_{i=1}^{n}f_ix_i$ is the sample mean of $X$, $N$ total number of observations, $s_x=\sqrt{V(x)}$ is the standard deviation of $X$, $s_x^2=V(x)=\dfrac{1}{N}\sum_{i=1}^{n}f_ix_i^2 -(\overline{x})^2$ is the variance of $X$ If …
