Questions: After correcting the error, the mean by and the median by . The was affected more.

Solution Steps

To solve this problem, we need to understand how correcting an error in a dataset affects the mean and median. First, calculate the original mean and median of the dataset. Then, correct the error and recalculate the mean and median. Compare the changes in both statistics to determine which was affected more.

The original dataset is \([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]\). To find the mean, sum all the numbers and divide by the count of numbers: \[ \text{Original Mean} = \frac{10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 + 100}{10} = 55.0 \] The median is the middle value of the ordered dataset. Since there are 10 numbers, the median is the average of the 5th and 6th numbers: \[ \text{Original Median} = \frac{50 + 60}{2} = 55.0 \]

The corrected dataset is \([10, 20, 30, 40, 50, 60, 70, 80, 90, 110]\). Recalculate the mean: \[ \text{Corrected Mean} = \frac{10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 + 110}{10} = 56.0 \] The median remains the same because the middle values (5th and 6th) are unchanged: \[ \text{Corrected Median} = \frac{50 + 60}{2} = 55.0 \]

Calculate the change in mean and median: \[ \text{Mean Change} = 56.0 - 55.0 = 1.0 \] \[ \text{Median Change} = 55.0 - 55.0 = 0.0 \]

Compare the absolute changes:

• Mean change: \(1.0\)
• Median change: \(0.0\)

The mean was affected more because the change in mean is greater than the change in median.

Final Answer