The data set shown below has an outlier. Determine the outlier and then fill out the chart.
Data: 5, 10, 12, 14, 18, 24, 60
If the outlier is excluded, what happens to:
Increase
Decrease
No effect
A
the median?
B
the mean?
C
the mode?
D
the range?
To determine the outlier, we can look for a value that is significantly different from the others. In the given data set, the value 60 is significantly larger compared to the other values, making it the outlier.
If the outlier is excluded:
A) the median:
The median is the middle value of the data set. Excluding the outlier, the values would be rearranged in ascending order: 5, 10, 12, 14, 18, 24. The median would be the average of the two middle values, which are 12 and 14. Thus, the median would decrease from 18 to 13.
B) the mean:
The mean is the average of all the values. Excluding the outlier, the sum of the values would be 5+10+12+14+18+24 = 83. There are 6 values (without the outlier), so the mean would be 83/6 ≈ 13.83. Thus, the mean would decrease from 20.57 to 13.83.
C) the mode:
The mode is the value(s) that appear most frequently in the data set. Excluding the outlier, there are no repeated values. The mode would remain the same, which is no effect.
D) the range:
The range is the difference between the largest and smallest values. Excluding the outlier, the largest value is 24 and the smallest value is 5. The range would decrease from 55 to 19. Thus, the range would decrease.