Remember that an outlier is an extremely high or extremely low value when compared with the rest of the values in the data set.
9.8
Practice makes perfect
We want to check whether there are any outliers. Let's start by defining some important characteristics of data sets.
Lower Quartile (Q1) is the median of the lower half of the data set.
Upper Quartile (Q3) is the median of the upper half of the data set.
Interquartile Range is the difference between the upper and lower quartiles (Q3-Q1).
Let's find the upper quartile, the lower quartile, and the interquartile range for the given data set. Do not forget to write the values in numerical order!
2.1, 2.3, 2.9, 3.0, 3.3, 3.4, 4.5, 5.9, 9.8We have two middle values for each half. This means that we need to calculate the mean of those middle values.
rr
Upper Quartile:& 4.5+ 5.9/2=5.2 [0.8em]
Lower Quartile:& 2.3+ 2.9/2=2.6 [0.8em]
Interquartile Range:& 5.2-2.6=2.6
An outlier is an extremely high or extremely low value when compared with the rest of the values in the set. To check for them, we look for data values that are beyond the upper or lower quartiles by more than 1.5 times the interquartile range.
Minimum=& Q1-IQR*1.5
Maximum=& Q2+IQR*1.5
Let's find the minimum and maximum for a value not to be an outlier.
Minimum
2.6-1.5* 2.6=-1.3 [0.5em]
Maximum
5.2+1.5* 2.6=9.1
Any value between -1.3 and 9.1 is not an outlier. All the numbers in the data set are positive. Therefore, they are all greater than - 1.3. This means that we only need to look for values greater than 9.1.
2.1, 2.3, 2.9, 3.0, 3.3, 3.4, 4.5, 5.9, 9.8
The data set has only one outlier, which is 9.8.
