Mode of the observations 10, 11, 16, 17, 12, 13, 17, 16, 12, 16, 10, 15, 16, 10 is

The mode is the value that occurs most often. Tally the 14 observations: 16 appears 4 times (positions 3, 8, 10, 13), 10 appears 3 times, 12 and 17 appear 2 times each, and 11, 13 and 15 appear once each. So 16 is the mode, and option C is correct.

Option A is wrong because 13 occurs only once. Option B is wrong because 15 also occurs only once. Option D fails because 16 is in the list.

Core concept: For ungrouped data, mode is found by frequency counting, not by size or position. A data set can have no mode, one mode, or several. In grouped data, the modal class is found first and the mode is then estimated with a formula. Mode matters most for categorical or survey data, such as the most preferred crop or the most common complaint in a district.

Trap: Aspirants often pick the value that looks repeated or the largest value on a quick glance, or they miscount the repeats of 10 and 16 in a long list. Write the tally down instead.