The data set shown below has an outlier. Determine the outlier and then fill in the chart.
Data: 5,10,12,14,18,24,60
If the outlier is excluded what happens to the median, mean, mode, and range?
To determine the outlier, we can analyze the data set and look for any values that significantly deviate from the others.
Data: 5, 10, 12, 14, 18, 24, 60
Observing the values, we can see that the number 60 is much larger than all the other values. Therefore, 60 is the outlier.
Now, let's fill in the chart:
Data (Outlier Excluded): 5, 10, 12, 14, 18, 24
- Median: The median is the middle value when the data set is arranged in ascending order. Since there are six numbers, the median is the average of the two middle numbers. Thus, excluding the outlier results in the median being (12 + 14)/2 = 13.
- Mean: The mean is calculated by summing up all the values and dividing by the number of values. Excluding the outlier, the sum of the remaining numbers is 5 + 10 + 12 + 14 + 18 + 24 = 83. There are 6 numbers remaining, so the mean is 83/6 = 13.83 (rounded to two decimal places).
- Mode: The mode represents the value(s) that appear the most in the data set. There is no change in the mode because none of the values repeat.
- Range: The range is the difference between the largest and smallest values in the data set. Excluding the outlier, the smallest value is 5, and the largest value is 24. Therefore, the range is 24 - 5 = 19.
In summary, excluding the outlier, the median is 13, the mean is 13.83, the mode remains the same, and the range is 19.
Does the mean, median, mode, and range increase, decrease, or have no effect without the outlier?
Apologies for the confusion in my previous response. Let's accurately determine the impact of excluding the outlier on the mean, median, mode, and range.
Data (Outlier Excluded): 5, 10, 12, 14, 18, 24
- Median: As mentioned earlier, the median is the middle value when the data set is arranged in ascending order. Since there are six numbers, the median is the average of the two middle numbers. Thus, excluding the outlier results in the median being (12 + 14)/2 = 13.
- Mean: The mean is calculated by summing up all the values and dividing by the number of values. Excluding the outlier, the sum of the remaining numbers is 5 + 10 + 12 + 14 + 18 + 24 = 83. There are 6 numbers remaining, so the mean is 83/6 = 13.83 (rounded to two decimal places).
- Mode: The mode represents the value(s) that appear the most in the data set. Excluding the outlier does not change the mode because none of the values repeat. In this case, there is no mode since all values appear only once.
- Range: The range is the difference between the largest and smallest values in the data set. Excluding the outlier, the smallest value is 5, and the largest value is 24. Therefore, the range is 24 - 5 = 19.
In summary, excluding the outlier, the mean increases from 17.14 to 13.83, the median remains the same at 13, the mode remains undefined (no mode), and the range decreases from 55 to 19.