Mean, median and mode Mean, median, mode are the measures of central tendency. They are also known as averages. Averages are the measures which condense a huge set of numerical data into a single numerical value which is representative of the entire data. They give us an idea about the concentration of the values in …
Karl Pearson coefficient of skewness for grouped data Let $(x_i,f_i), i=1,2, \cdots , n$ be given frequency distribution. The Karl Pearson’s coefficient skewness is given by $S_k =\dfrac{Mean-Mode}{sd}=\dfrac{\overline{x}-\text{Mode}}{s_x}$ OR $S_k =\dfrac{3(Mean-Median)}{sd}=\dfrac{3(\overline{x}-M)}{s_x}$ where, $\overline{x}$ is the sample mean, $M$ is the median, $s_x$ is the sample standard deviation. Sample mean The sample mean $\overline{x}$ is given …
Skewness Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A data set is symmetric if it looks the same to the left and right of the center point. The data set is said to be skewed if it is not symmetric. The data set is said to be positively (negatively) …
Mean absolute deviation Calculator Use this calculator to find the Mean Absolute Deviation using frequency distribution (uniform or discrete),frequencies and grouped data Mean absolute deviation is another measure of dispersion. MAD is an absolute measure of dispersion. Let $(x_i,f_i), i=1,2, \cdots , n$ be given frequency distribution. The mean of $X$ is denoted by $\overline{x}$ …
Five number summary for ungrouped 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. 5 number summary includes five values, namely, minimum value ($\min$), first quartile ($Q_1$), $\text{median }$ ($Q_2$), third quartile ($Q_3$), maximum value ($\max$). The five …
Deciles for grouped data Deciles are the values which divide whole distribution into ten equal parts. They are 9 in numbers namely $D_1, D_2, \cdots, D_9$. Here $D_1$ is first decile, $D_2$ is second decile and so on. The formula for $i^{th}$ decile is $$ \begin{aligned} D_i=l + \bigg(\frac{\frac{iN}{10} – F_
Deciles for ungrouped data Deciles are the values of arranged data which divide whole data into ten equal parts. They are 9 in numbers namely $D_1,D_2, \cdots, D_9$. Here $D_1$ is first decile, $D_2$ is second decile, $D_3$ is third decile and so on. The formula for $i^{th}$ decile is $D_i =$ Value of $\bigg(\dfrac{i(n+1)}{10}\bigg)^{th}$ …
Bowley’s Coefficient of Skewness for grouped data Bowley’s coefficient of skewness is based on quartiles of the data. It is based on the middle 50 percent of the observations of data set. It means the Bowley’s coefficient of skewness leaves the 25 percent observations in each tail of the data set. For a symmetric distribution, …
Kurtosis Kurtosis is the peakedness of a frequency curve. Even if two curves have the same average, dispersion and skewness, one may have higher (or lower) concentration of values near the mode, and in this case, its frequency curve will show a sharper peak (or flatter peak) than the other. This characteristics of a frequency …
Moment coefficient of kurtosis for grouped data Let $(x_i,f_i), i=1,2, \cdots , n$ be given frequency distribution. The mean of $X$ is denoted by $\overline{x}$ and is given by $$ \begin{eqnarray*} \overline{x}& =\frac{1}{N}\sum_{i=1}^{n}f_ix_i \end{eqnarray*} $$ The moment coefficient of kurtosis (also known as Pearson’s moment coefficient of kurtosis) is denoted by $\beta_2$ and is defined …
