When n is large, the binary search takes much less time, in the worst case, than the linear search. This is because it makes 1g n rather than n comparisons, going through its loop body 1g n rather than n times. However, the steps performed in the loop body of the binary search are more complex and more time-consuming than the steps performed in the loop body for the linear search. Hence it is possible, for smaller values of n, that the linear search will be faster. Similarly, the interpolation search will need to perform more complex steps in its loop body, even though it may need to loop fewer times than the binary search.
Of course the binary and extrapolation searches require sorted data. When only a few searches are to be made or when n is small, it may not pay to spend time to sort the data first. For repeated searching or large n, the efficiencies of the binary and extrapolation searches easily overcome the cost of sorting.