What are outliers and how it can be identified in a given dataset?
Heart rates of 11 student in beats per minute
64,74,84,84,94,94,94,104,104,114,114.
Outliers are data points that significantly differ from the other values in a dataset. An outlier can be an unusually high or low value compared to the rest of the data points.
To identify outliers in a given dataset, one commonly used method is the use of the interquartile range (IQR). The IQR measures the dispersion of the dataset by calculating the difference between the third quartile (Q3) and the first quartile (Q1).
To identify outliers using the IQR method:
1. Sort the data points in ascending order: 64, 74, 84, 84, 94, 94, 94, 104, 104, 114, 114.
2. Calculate Q1, which represents the 25th percentile. In this case, Q1 = 84.
3. Calculate Q3, which represents the 75th percentile. In this case, Q3 = 104.
4. Calculate the IQR by subtracting Q1 from Q3. In this case, IQR = 104 - 84 = 20.
5. Determine the lower bound and upper bound for outliers. The lower bound is Q1 - 1.5 * IQR, and the upper bound is Q3 + 1.5 * IQR.
- Lower bound = 84 - 1.5 * 20 = 54
- Upper bound = 104 + 1.5 * 20 = 134
6. Any data point below the lower bound or above the upper bound is considered an outlier.
In the given dataset, there are no outliers since all the values (64, 74, 84, 84, 94, 94, 94, 104, 104, 114, 114) lie within the range of the lower and upper bounds.