🔢 Mode

• Ungrouped data: tally each value and pick the one with the highest count. To save time, only count the numbers that appear in the answer options.

• Find a hidden value: for “choose $k$ so the mode is M”, count the rivals first, then make M occur more often than any of them (usually one extra time).

• Grouped data (class intervals): the modal class is the class with the highest frequency, and the mode is interpolated inside it:

$\text{Mode}=l+\dfrac{f_1-f_0}{2f_1-f_0-f_2}\times h$

where $l$ = lower limit of the modal class, $f_1$ = its frequency, $f_0$ = the class before, $f_2$ = the class after, and $h$ = class width. The mode always lands inside the modal class, so options outside it can be struck off at once.

• Discrete table trap: if the table lists single x-values (not intervals), the mode is simply the x-value with the biggest frequency — no formula, and never the frequency itself.