To identify outliers using the Interquartile Range (IQR) method, we'll follow these steps:
1. Determine the first (Q1) and third quartiles (Q3):
From the given five-number summary, Q1 is 38 and Q3 is 52.
2. Calculate the Interquartile Range (IQR):
The IQR is calculated as [tex]\( Q3 - Q1 \)[/tex].
[tex]\[
IQR = 52 - 38 = 14
\][/tex]
3. Calculate the lower and upper bounds for identifying outliers:
- The lower bound is calculated as [tex]\( Q1 - 1.5 \times IQR \)[/tex].
- The upper bound is calculated as [tex]\( Q3 + 1.5 \times IQR \)[/tex].
[tex]\[
\text{Lower bound} = 38 - 1.5 \times 14 = 38 - 21 = 17
\][/tex]
[tex]\[
\text{Upper bound} = 52 + 1.5 \times 14 = 52 + 21 = 73
\][/tex]
4. Identify outliers:
Any value below the lower bound (17) or above the upper bound (73) is considered an outlier.
Given the tails of the distribution:
[tex]\[
11, 16, 24, 26, 27, 60, 61, 61, 62, 67
\][/tex]
We compare each value to the bounds:
- 11 is less than 17, so it is an outlier.
- 16 is less than 17, so it is an outlier.
- 24, 26, 27, 60, 61, 61, 62, and 67 are all within the range 17 to 73, so they are not outliers.
Thus, the identified outliers are:
- 11
- 16
These are the values in the tails that are identified as outliers using the IQR method.
