To determine which value in the dataset is an outlier, we can look at the distribution of the values. The data you provided consists of the following numbers:
{176, 152, 18, 176, 136, 184, 181, 176}
- Minimum Value: 18
- Maximum Value: 184
- Range: 184 - 18 = 166
Now we can compute the median and the quartiles to identify any outliers.
Sort the dataset:
{18, 136, 152, 176, 176, 176, 181, 184}
The median (Q2) is the average of the 4th and 5th numbers (176 + 176) / 2 = 176.
The first quartile (Q1 - the median of the lower half) is the average of 136 and 152 → (136 + 152) / 2 = 144.
The third quartile (Q3 - the median of the upper half) is the average of 176 and 181 → (176 + 181) / 2 = 178.5.
Now we can determine the interquartile range (IQR):
IQR = Q3 - Q1 = 178.5 - 144 = 34.5.
To identify outliers, we can set the following boundaries:
- Lower bound: Q1 - 1.5 * IQR = 144 - (1.5 * 34.5) = 144 - 51.75 = 92.25.
- Upper bound: Q3 + 1.5 * IQR = 178.5 + (1.5 * 34.5) = 178.5 + 51.75 = 230.25.
Any value below 92.25 or above 230.25 is considered an outlier.
In the dataset, the only number that falls below 92.25 is 18. Therefore, 18 is the outlier.
So the answer is 18.