Final answer:
The correct answer is '2'. By removing the number 2 from the original list, the mean, mode, and median of the remaining numbers are all equal to 5.
Step-by-step explanation:
The student has provided a sequence of numbers (2, 3, 4, 5, 5, 5, 5, 5, 6, 7) and wants to determine which number, when removed, leaves the remaining sequence with the mean, mode, and median all being equal. By examining the sequence, one can see that the number 5 is the mode since it occurs more frequently than any other number.
Next, we calculate the mean of the sequence: (2 + 3 + 4 + 5 + 5 + 5 + 5 + 5 + 6 + 7) / 10 = 4.7. The median of the ten numbers is the average of the 5th and 6th terms (since there's an even number of terms), which are both 5. Removing any '5' from the list would result in the mode and median still being 5. We must also ensure the mean of the new list is 5. To check this, we remove one 5 and calculate the new mean: (2 + 3 + 4 + 5 + 5 + 5 + 5 + 6 + 7) / 9 = 4.67, which is not equal to the mode or median.
However, if we remove the '2' instead, the new mean of the sequence becomes (3 + 4 + 5 + 5 + 5 + 5 + 5 + 6 + 7) / 9 = 5, which equals the mode and median. Therefore, the number removed to make the mean, median, and mode all equal is 2.