Answer :
The outlier in the set of data values 19.2, 19.8, 25.9, 18.1, 36.9, 23.3, 15.7, 21.4, 61.3, and 28.6 is 61.3.
To identify the outlier, we need to find the value that is significantly different from the other values in the data set.
One way to do this is by using the interquartile range (IQR). The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
First, we need to find Q1 and Q3. To do this, we need to order the data set in ascending order: 15.7, 18.1, 19.2, 19.8, 21.4, 23.3, 25.9, 28.6, 36.9, and 61.3.
Next, we find the median (Q2) which is the middle value in the data set. In this case, Q2 is 21.4.
To find Q1, we take the median of the lower half of the data set, which is 18.1.
To find Q3, we take the median of the upper half of the data set, which is 28.6.
Now we can calculate the IQR:
IQR = Q3 - Q1 = 28.6 - 18.1 = 10.5.
Finally, we can determine the outlier by using the 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, Q1 - 1.5 * IQR = 18.1 - 1.5 * 10.5 = 2.85, and
Q3 + 1.5 * IQR = 28.6 + 1.5 * 10.5 = 45.35.
Since 61.3 is greater than 45.35, it is considered an outlier.
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