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 compare each data point to the rest of the data set and identify any values that are significantly higher or lower than the others. In this case, the value 60 is the outlier as it is much larger than the other data points.
If the outlier is excluded, the chart would look like this:
Data: 5, 10, 12, 14, 18, 24
A. The median would increase. The median is the middle value when the data set is arranged in ascending order. In this case, the median is 14. However, if the outlier 60 is excluded, the new median would be 13 (the average of 12 and 14), which is higher than the previous median.
B. The mean would decrease. The mean is calculated by summing up all the values and dividing by the total number of values. In this case, the mean is (5 + 10 + 12 + 14 + 18 + 24 + 60)/7 = 18.86. However, if the outlier 60 is excluded, the new mean would be (5 + 10 + 12 + 14 + 18 + 24)/6 = 14.83, which is lower than the previous mean.
C. The mode would have no effect. The mode is the value that appears most frequently in the data set. In this case, all the values appear only once, so there is no mode. Excluding the outlier would not change this.
D. The range would decrease. The range is the difference between the highest and lowest values in the data set. In this case, the range is 60 - 5 = 55. However, if the outlier 60 is excluded, the new range would be 24 - 5 = 19, which is lower than the previous range.