Use the following data set to answer this question:
14, 17, 13, 15, 14, 19, 2, 18
What is the outlier?
*
14
17
13
15
19
2
18
There is not an outlier in this data set
There is not an outlier in this data set.
To find the outlier in a data set, we can use the concept of the interquartile range (IQR).
First, let's sort the data set in ascending order: 2, 13, 14, 14, 15, 17, 18, 19.
Next, we need to find the first quartile (Q1) and the third quartile (Q3).
To find Q1, we need to find the median of the lower half of the data set. In this case, the lower half is: 2, 13, 14, 14.
Since there are an even number of data points, we take the average of the two middle values: (13 + 14) / 2 = 13.5. Therefore, Q1 = 13.5.
To find Q3, we need to find the median of the upper half of the data set. In this case, the upper half is: 15, 17, 18, 19.
Again, since there are an even number of data points, we take the average of the two middle values: (17 + 18) / 2 = 17.5. Therefore, Q3 = 17.5.
Now, we can calculate the IQR by subtracting Q1 from Q3: 17.5 - 13.5 = 4.
To determine if there is an outlier, we can use the following rule: any value that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.
In this case, the values that are less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR are: 2.
Therefore, the outlier in this data set is 2.