Find the median of 8, 10, 19, 23, 26, 34, 40, 41, 41, 48, 51, 55, 70, 84, 91, 92. (i) If we include one value to the data (in the given list) without affecting the median, what could that value be? (ii) If we include two values to the data without affecting the median what could the two values be? (iii) If we remove one value from the data without affecting the median what could the value be?
A value equal to 41 (the current median) can be added without affecting the median.
Two values that are both 41, or one value less than 41 and one value greater than 41 (symmetric around the median), can be added without affecting the median.
Removing one of the two 41s will not affect the median, as one 41 will still remain in the middle position.
Explanation
(i) Adding 41 keeps the middle positions unchanged since the median is already 41. (ii) Adding values symmetrically around the median or adding duplicate median values preserves the median. (iii) Since there are two 41s at the middle positions, removing one still leaves 41 as the median.