In: Computer Science
Let the data range be
201,199, 269, 236, 278, 271, 303, 291, 283, 301, 341
Therefore n = 11
Median(Q2) = 1/2(11+1)th term = 6th term
Q2 = 271
Lower Quartile(Q1) = 1/4(11+1)th term = 3rd term
Q1 = 269
Upper Quartile (Q3) = 3/4(11+1) th term = 9th term
Q3 = 283
Inter Quartile Range (IQR) = Q3 – Q1 = 283 – 269
IQR = 14
Lower Limit = Q1 – 1.5 IQR = 269 – 1.5 (14)
Lower Limit = 248
Upper Limit = Q3 + 1.5 IQR = 283 + 1.5 (14)
Upper Limit = 304
Hence it is clear that any range above 304 and below 248 are outliers.Hence in the data series 201,199, 269, 236, 278, 271, 303, 291, 283, 301, 341, outliers are 201, 199 and 341. These 3 values which lies on either of the extremes can be considered abnormal and should be discarded from the entire series so that any analysis made on this series is not influenced by these extreme values. So the data series that should be considered for further observation or study after discarding the outliers are as below.
269, 236, 278, 271, 303, 291, 283, 301