The median of a set of 11 distinct observations is 73.2. If each of the largest five observations of the set is increased by 3, then the median of the new set:

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Accepted Answer

**Solution:**

1. The median of 11 observations is the 6th observation when the data is arranged in ascending order.

2. Let the observations be ordered as:
   $$O_1, O_2, O_3, O_4, O_5, O_6, O_7, O_8, O_9, O_{10}, O_{11}$$

3. The median is the value of $$O_6 = 73.2$$.

4. The largest five observations are $$O_7, O_8, O_9, O_{10}, O_{11}$$.

5. Increasing each of these five observations by 3 changes them to:
   $$O_7 + 3, O_8 + 3, O_9 + 3, O_{10} + 3, O_{11} + 3$$

6. The new set becomes:
   $$O_1, O_2, O_3, O_4, O_5, O_6, (O_7 + 3), (O_8 + 3), (O_9 + 3), (O_{10} + 3), (O_{11} + 3)$$

7. The 6th observation $$O_6$$ remains unchanged.

8. Since the median is the middle value (6th observation), and it is not changed, the median of the new set remains the same.

**Answer:** remains the same as that of the original set

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