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 …
Mean absolute deviation for ungrouped data Mean absolute deviation is another measure of dispersion. MAD is an absolute measure of dispersion. Let $x_i, i=1,2, \cdots , n$ be $n$ observations. The mean of $X$ is denoted by $\overline{x}$ and is given by $$ \begin{eqnarray*} \overline{x}& =&\frac{1}{n}\sum_{i=1}^{n}x_i \end{eqnarray*} $$ The mean absolute deviation about mean is …
Percentiles for grouped data Percentiles are the values which divide whole distribution into hundred equal parts. They are 99 in numbers namely $P_1, P_2, \cdots, P_{99}$. Here $P_1$ is first percentile, $P_2$ is second percentile and so on. For discrete frequency distribution, the formula for $i^{th}$ percentile is $P_i =\bigg(\dfrac{i(N)}{100}\bigg)^{th}$ value, $i=1,2,\cdots, 99$ where, $N$ …
Octiles for grouped data Octiles are the values of arranged data which divide whole data into eight equal parts. They are 7 in numbers namely $O_1,O_2, \cdots, O_7$. Here $O_1$ is first octile, $O_2$ is second octile, $O_3$ is third octile and so on. For discrete frequency distribution, the formula for $i^{th}$ octile is $O_i …
Quartiles Calculator for grouped data Use this calculator to find the Quartiles for grouped (frequency distribution) data. Quartiles Calculator (Grouped Data) Type of Freq. Dist. DiscreteContinuous Enter the Classes for X (Separated by comma,) Enter the frequencies (f) (Separated by comma,) Calculate Results Number of Obs. (N): First Quartile : ($Q_1$) Second Quartile : ($Q_2$) …
Inter Quartile Range for Grouped Data Calculator Use this calculator to find the Inter Quartile Range for grouped (frequency distribution) data. Calculator Inter Quartile Range Calculator (Grouped Data) Type of Frequency Distribution DiscreteContinuous Enter the Classes for X (Separated by comma,) Enter the frequencies (f) (Separated by comma,) Calculate Results Number of Observation (N): First …
