What happens to the mean, median and mode for the data shown if the outlier is eliminated?
8 3 5 3 23 4 7
The mean becomes lower.
What do you think happens to the median and the mode?
the median becomes higher?
Right.
To find out what happens to the mean, median, and mode when an outlier is eliminated, we first need to calculate the mean, median, and mode for the given data set.
Given data: 8, 3, 5, 3, 23, 4, 7
Mean:
To find the mean, we need to sum up all the numbers in the data set and divide it by the total count of numbers.
Mean = (8 + 3 + 5 + 3 + 23 + 4 + 7) / 7
= 53 / 7
= 7.5714 (rounded to four decimal places)
Median:
To find the median, we need to arrange the numbers in ascending order and find the middle number.
Arranging the numbers in ascending order: 3, 3, 4, 5, 7, 8, 23
The middle number(s) is the median. In this case, we have two middle numbers, 5 and 7. Therefore, the median is (5 + 7) / 2 = 6.
Mode:
The mode is the number that appears most frequently in the data set. In this case, the number 3 appears twice, making it the mode.
Now, let's eliminate the outlier, which is the number 23, and recalculate the mean, median, and mode of the revised data set.
Revised data: 8, 3, 5, 3, 4, 7
Mean:
Mean = (8 + 3 + 5 + 3 + 4 + 7) / 6
= 30 / 6
= 5
Median:
Arranging the numbers in ascending order: 3, 3, 4, 5, 7, 8
The middle number(s) is the median. In this case, we have two middle numbers again, 4 and 5. Therefore, the median is (4 + 5) / 2 = 4.5.
Mode:
The mode remains the same since the number 3 still appears twice.
In summary, if the outlier (23) is eliminated from the data set, the mean decreases from 7.5714 to 5, the median decreases from 6 to 4.5, and the mode remains the same, which is 3.