To identify potential outliers in a data set using the quartiles and median, you can calculate the interquartile range (IQR) and then determine if any data points fall significantly below the first quartile (Q1 - 1.5 * IQR) or significantly above the third quartile (Q3 + 1.5 * IQR). The IQR is the range between the first quartile (Q1) and the third quartile (Q3).
In this case:
- Median (Q2) = 55
- First Quartile (Q1) = 50
- Third Quartile (Q3) = 70
Calculate the IQR:
IQR = Q3 - Q1 = 70 - 50 = 20
Now, use the IQR to determine the potential outliers:
Lower Bound = Q1 - 1.5 * IQR = 50 - 1.5 * 20 = 50 - 30 = 20
Upper Bound = Q3 + 1.5 * IQR = 70 + 1.5 * 20 = 70 + 30 = 100
So, any data points less than 20 or greater than 100 are potential outliers.
Among the given options:
- Option 1: Data points less than 40 and greater than 80 are potential outliers. This option is not entirely correct, as it uses different values (40 and 80) as the thresholds.
- Option 2: Data points less than 35 and greater than 85 are potential outliers. This option is also not entirely correct; the thresholds should be 20 and 100 based on the calculated values.
- Option 3: Data points less than 45 and greater than 75 are potential outliers. This option is not entirely correct; the thresholds should be 20 and 100 based on the calculated values.
- Option 4: Data points less than 30 and greater than 90 are potential outliers. This option correctly identifies the potential outliers based on the calculated values.
So, **Option 4** is the correct choice for identifying the potential outliers in the data set.