What happens to the mean, median and mode for the data shown if the outlier is eliminated? 38 33 38 32 33 6b 30
Is the outlier supposed to be 6? 6b? 60?
the outlier is suppose to be 6
The mean must increase, right?
What would happen to the mode and median?
To analyze the impact of eliminating an outlier on the mean, median, and mode of a data set, we first need to identify and remove the outlier from the given data set: 38, 33, 38, 32, 33, 6b, 30.
However, before we proceed, it's important to note that the value "6b" seems to be a typographical error or an unknown value. We cannot include it in our analysis without knowing its correct representation or if it's a valid data point. Consequently, we will calculate the mean, median, and mode without considering this unknown value.
Here's how we can determine the impact on each measure:
1. Mean: The mean is the average value of the data set. To calculate the mean, add up all the numbers and divide by the total count.
Sum of the data set with the unknown value: 38 + 33 + 38 + 32 + 33 + 6b + 30 = 6b + 204
Total count with the unknown value: 7
To remove the unknown value, subtract "6b" from the sum: (6b + 204) - 6b = 204
Now divide the sum by the reduced count: 204 / 6 = 34
Therefore, the mean of the data set without the outlier is 34.
2. Median: The median is the middle value when the data set is arranged in ascending order. To find the median, we sort the data set and identify the value in the middle.
Data set with the unknown value in ascending order: 30, 32, 33, 33, 38, 38, 6b
After removing the unknown value, the updated data set in ascending order is: 30, 32, 33, 33, 38, 38
As there is an even number of values (6), the median is the average of the two middle values. In this case, the middle values are 33 and 33. The median is therefore (33 + 33) / 2 = 33.
Thus, the median of the data set without the outlier remains 33.
3. Mode: The mode is the value(s) that appear most frequently in the data set. If there are no repeated values or if there is an even number of modes, the data set is said to have no mode(s).
Data set with the unknown value: 38, 33, 38, 32, 33, 6b, 30
After removing the unknown value, the updated data set is: 38, 33, 38, 32, 33, 30
In this case, the mode(s) would be the value(s) that have the highest frequency. Here, both 38 and 33 appear twice in the data set, making them the modes.
Therefore, the modes of the data set without the outlier are 38 and 33.
In summary, if we eliminate the outlier from the given data set, the mean becomes 34, the median remains 33, and the modes are 38 and 33.