Examine the statements below and justify if the statement is always true, sometimes true, or never true. (i) Removing a value less than the median will decrease the median. (ii) Including a value less than the mean will decrease the mean. (iii) Including any 4 values will not affect the median. (iv) Including 4 values less than the median will increase the median.
Sometimes true. The effect depends on whether the removed value affects the middle positions in the sorted data.
Always true. When a value less than the current mean is added, the new mean will be lower than before.
Sometimes true. It depends on where the 4 values are positioned relative to the median and the original data count.
Sometimes true. Adding values below the median can shift the middle position, but the effect depends on the original data structure.
Explanation
(i) The chapter shows that removing a value less than the median may or may not change the median depending on its position relative to the middle values. (ii) The chapter demonstrates that including a value smaller than the mean causes the mean to decrease to maintain balance. (iii) Adding 4 values may or may not shift the middle positions depending on their values and positions. (iv) The chapter explains that adding values less than the median tends to shift the median position, but the exact effect varies.