To solve this question, we need to update the statistical measures—mean, median, and mode—after including a new student aged 45. I'll walk you through the general process for each part.

Given Information:

We do not have the original set of ages, so I’ll explain how each value is calculated, and you can input the original data to find the results.

1. Mean is the average of all data points.

   • New mean: After adding the new age (45), we recalculate the mean as follows: $\text{New Mean} = \frac{\text{sum of original ages} + 45}{\text{number of original students} + 1}$

2. Median is the middle value when the data set is ordered.

   • If the new age changes the order, find the new middle value.
   • If the total number of students is odd, the median will be the middle number. If it’s even, the median will be the average of the two middle numbers.

3. Mode is the most frequently occurring number in the data set.

   • If the new age of 45 appears frequently, it could become the mode. Otherwise, check if the mode remains the same.

4. Comparing Changes:

   • After recalculating the mean, median, and mode, determine which value had the largest absolute change.

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Let's go over each part:

i. New Mean:

You need the sum of the original ages and the number of students to calculate the new mean using the formula above.

ii. New Median:

You would need to add 45 to the list of ages, sort them, and then find the middle value (or average of two middle values if the count is even).

iii. New Mode:

If 45 doesn't repeat in the data set, the mode will remain unchanged from the original data set. If 45 becomes the most frequent age, it will be the new mode.

iv. Value That Changed the Most:

To determine this, calculate the absolute change in the mean, median, and mode, and compare which changed the most.

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Do you have the original data so I can give precise answers? If not, I can help guide you further.