In the data set: (4, 20, 21, 25, 36, 22, 6, 34) are there any outliers?
To determine if there are any outliers in the data set (4, 20, 21, 25, 36, 22, 6, 34), we can use the interquartile range (IQR) rule.
1. First, we need to calculate the first quartile (Q1) and the third quartile (Q3) of the data set.
- Arranging the data in ascending order: (4, 6, 20, 21, 22, 25, 34, 36)
- Q1 = 11.5 (average of the 2nd and 3rd values in the ordered data)
- Q3 = 29.5 (average of the 6th and 7th values in the ordered data)
2. Next, we calculate the IQR by subtracting Q1 from Q3.
- IQR = Q3 - Q1 = 29.5 - 11.5 = 18
3. To identify any outliers, we can consider any data point that is more than 1.5 times the IQR below Q1 or above Q3 to be an outlier.
- Lower outlier threshold = Q1 - 1.5*IQR = 11.5 - 1.5*18 = -5.5
- Upper outlier threshold = Q3 + 1.5*IQR = 29.5 + 1.5*18 = 57.5
4. Comparing the thresholds to the data set, we can conclude that there are no outliers since all the data points fall within the range (-5.5, 57.5).
Therefore, there are no outliers in the data set (4, 20, 21, 25, 36, 22, 6, 34).