Final answer:
Halving the smallest value in a data set of all positive values results in the mean of the data set decreasing, but it does not affect the interquartile range or the range, and the standard deviation is likely to decrease.
Step-by-step explanation:
The question pertains to the effects of modifying the smallest value in a data set of all positive values on certain statistical measures. Given that the smallest value is halved, the only true outcome among the options given is that the mean decreases.
Halving the smallest value does not affect the interquartile range (IQR), as IQR is dependent on the quartiles which wouldn't change unless the smallest value was also a quartile, which wasn't specified in the question. The range would stay the same since it's determined by the difference between the maximum and minimum values and halving the minimum does not bring it nearer to the maximum value. Additionally, the standard deviation is likely to decrease due to the reduction of the squaring effect on the smallest value when calculating variance.