Which of the following is not changed for the observations (where lies between \

We have observations: 31, 48, 50, 60, 25, 8, 3x, 26, 32, where x lies between 10 and 15, so 3x is between 30 and 45. The sorted order depends on the exact value of 3x, but the minimum (8) and maximum (60) are fixed, so the range (60-8=52) is unchanged. The median changes: it is 31 if 3x ≤ 31, 3x if 31 < 3x < 32, and 32 if 3x ≥ 32. The arithmetic mean (280+3x)/9 changes with x. For quartile deviation (Q.D.), Q1 is the median of the first four numbers, which are always 8, 25, 26, and either 31 or 3x (but 3x ≥ 30, so the median is always (25+26)/2 = 25.5). Q3 is the median of the last four numbers, which are always 32, 48, 50, 60 or 3x, 48, 50, 60 (since 3x ≤ 45, the median is (48+50)/2 = 49). Thus Q.D. = (49 - 25.5)/2 = 11.75, constant. Therefore, both range and Q.D. are unchanged, but only Q.D. is listed as an option that is not changed (range is also not changed, but the question asks for which is not changed, and among A, B, C, D, D is the answer corresponding to Q.D.).