Maria recorded the number of hours each of her friends spent watching television last week.
4,17,15,17,14,17
If Maria removes the outliner from her list, which of the following will not change?
A. mean
B, median
C. mode
D. range
mode
To determine which of the following will not change if Maria removes the outlier from her list, let's first find the outlier.
An outlier is a value in a dataset that is significantly different from other values. In this case, we can see that the number 17 appears three times, while all other numbers are significantly lower. Therefore, we can conclude that 17 is the outlier.
Now, let's calculate the mean, median, mode, and range before removing the outlier:
Mean: The mean is calculated by summing up all the numbers and dividing it by the total count.
(4 + 17 + 15 + 17 + 14 + 17) / 6 = 84 / 6 = 14
Median: The median is the middle number when the numbers are arranged in ascending order.
Arranging the numbers in ascending order: 4, 14, 15, 17, 17, 17
The median is 15.
Mode: The mode is the number that appears most frequently in the dataset.
In this case, the mode is 17 since it appears three times.
Range: The range is the difference between the highest and lowest numbers in the dataset.
The highest number is 17, and the lowest number is 4, so the range is 17 - 4 = 13.
Now, let's remove the outlier (17) and calculate the mean, median, mode, and range again:
Mean: (4 + 15 + 14) / 3 = 33 / 3 = 11
Median: Arranging the numbers in ascending order: 4, 14, 15
The median is 14.
Mode: The mode remains the same since 17 was the mode before removing the outlier.
Range: The highest number is still 17, and the lowest number is 4, so the range remains the same at 17 - 4 = 13.
Based on the calculations, we can conclude that removing the outlier (17) will not change the mode, so the correct answer is C. mode.