The mode and median of a set of 7 observations are 22.72 and 49.28, respectively. If each of the largest 3 observations of the set is increased by 4, then the median of the new set?

The set contains 7 observations with mode = 22.72 and median = 49.28.

For 7 observations arranged in order, the median is the 4th value (middle position with 3 values below and 3 values above).

Therefore, the 4th observation = 49.28

Arranging the observations in order:

1st ≤ 2nd ≤ 3rd ≤ 4th ≤ 5th ≤ 6th ≤ 7th

The 4th value = 49.28 (median)

The largest 3 observations are the 5th, 6th, and 7th values.

When each is increased by 4, the new arrangement becomes:

1st ≤ 2nd ≤ 3rd ≤ 4th ≤ (5th+4) ≤ (6th+4) ≤ (7th+4)

The median of the new set is still the 4th value in the ordered arrangement.

The 4th value remains unchanged at 49.28, since only the 5th, 6th, and 7th values were modified.

Therefore, the new median = 49.28

The median remains the same as that of the original set.