The mode is simply the value that appears most often in a given data set. In this data set the value 77 appears three times. The value 68 appears twice. No other value appears more than once, which means 77 is the mode.

You may want to arrange the values in numerical order if it helps you see the repeating values, but it isn't required.

The mode of a data set is the element that appears most frequently; a data set with no mode has all of its elements appear exactly once.

All of the integers from 1 to 10 except for 5 are known to appear in this data set at least once. If \(\displaystyle N\) is equal to any of those integers, it is the only one repeated, and it is the mode. Only if \(\displaystyle N = 5\) can the set not have a repeated value. That makes this the correct choice.

The mode of a data set is the element that appears most frequently. In this set, that element is \(\displaystyle 7\), which appears three times. No other element appears more than twice.

The mode of a data set is the element that appears the most frequently. When two numbers both appear most frequently, there are two modes:

\(\displaystyle 5 \textrm{ and }7\)

The mode is the value that appears most often or has more frequency which is \(\displaystyle 77\) in this problem. The total number of data values are \(\displaystyle 7+3+4+1=15\). Since the number of values is odd, the median is the single middle value which is the \(\displaystyle 8th\) value in this problem. So the median is \(\displaystyle 79\).

The mode is the value that has more frequency in a given set of data than other values. Among the given frequencies in this problem, \(\displaystyle 90\) has the frequency of \(\displaystyle 22\) which is more than others. If \(\displaystyle 120\) is the mode, its frequency must be more than \(\displaystyle 22\).

The mode is the value that appears most often which is \(\displaystyle 80\ in\) in this data set, because \(\displaystyle 80\ in\) appears two times while all of the other values only appear one time.

The mode is the value that appears most often or has more frequency in a given set of data. So in this problem, the mode is \(\displaystyle 74\) which occurs most frequently.

If \(\displaystyle N \in \left \{ 4,6\right \}\) then the value of \(\displaystyle N\) is appears five times, more than any other element. This would give the set one mode.

If \(\displaystyle N \in \left \{ 2,7,8,10\right \}\), then 4, 6, and the value of \(\displaystyle N\) would appear three times each, more than any other element. This would give the set three modes.

If \(\displaystyle N\) assumes any other value, then 4 and 6 would appear three times each, more than any other element. This would give the set two modes.

Therefore, there are only two values of \(\displaystyle N\) that would give the set one mode.

If \(\displaystyle N \in \left \{ 4,6\right \}\), then the value of \(\displaystyle N\) will occur in the set five times, more than any other element. This will give the set one mode.

If \(\displaystyle N \in \left \{ 2,7,8,10\right \}\), then there will be three elements - \(\displaystyle 4,6,N\)  - that occur three times, more than any other element. This will give the set three modes.

If \(\displaystyle N\)is any other number, then there will be two elements - \(\displaystyle 4, 6\) - that occur twice, more than any other number. This will give the set two modes. 

Therefore, \(\displaystyle N \notin \left \{ 2,4,6,7,8,10\right \}\), and any other value of \(\displaystyle N\) gives the set one mode.