The Outliers in a series of data may correspond to extremely low or extremely high values and may result in a skewed distribution and may affect the normality of the data. In the presence of Outliers, the relationship studied between any two variables like income and expenditure may alter significantly. It is therefore essential to know how to identify the Outliers in a data set and how to treat them for further analysis.
For the present study, three method are used for the detection of the Outliers from the selected three normal samples of size 15, 20 and 25. According to selected three methods to identify the Outliers, the Lower Fence (LF) and Higher Fence values are defined as follows: IQR-Old Method: LF = Q1 – 1.5*IQR and HF= Q3+ 1.5* IQR. IQR-Takiar method: LF = Q1 – IQR*[0.25*ln(n)+0.20] and HF= Q3+ IQR*[0.25*ln(n)+0.20]. SD-Range-Takiar method: LF= Mean - SD*(0.37*ln (n) + 0.86) and
HF = Mean + SD*(0.37*ln (n) + 0.86). where n is the sample size. None of the methods showed the presence of Outliers in the initially selected samples of size 15, 20 and 25. For each initial sample, the minimum and maximum values are replaced by still lower and higher values thereby defining the new 10 samples with Outliers. For the study purposes, any value lying outside the range of each initial sample is assumed to be an Outlier. The Percentage detection rate of Outliers by the IQR-Old, SD-Range-Takiar method and IQR-Takiar method is 42%, 80% and 100%, respectively. The IQR-Takiar method is observed to be the superior method as compared to other two methods in detecting the Outliers and therefore, recommended to be used for identification of Outliers in the samples.
KEY WORDS: IQR-Old method, IQR-Takiar method, SD-Range-Takiar method, Outliers, Outlier detection rate