The mode of a set is the element that occurs in the set most frequently. A set without any repeated element is considered to have no mode.

For there to be a mode in the set , it must hold that ; the value of  is the mode of this set. Similarly, ..

If , then, in the set , two of the elements in  appear twice, giving the set two modes. If , then the value they are equal to appears three times as opposed to the other values, which appear one time each. That gives the set exactly one mode. 

The mode of a set is the element that occurs in the set most frequently; a set is bimodal if two elements tie for this.

Consider . If , then 1 and  each appear twice, more than any other element; this makes the set bimodal.  If , the set has one mode, 1, since it appears three times, more than any other element. If  has any other value, then the set has one mode, 1.  Therefore, . For similar reasons, . Therefore, .

The "stem" of this data set represents the tens digits of the data values; the "leaves" represent the units digits. 

The range of a data set is the difference of the high and low values. The highest value represented is 87 (7 is the last "leaf" in the bottom, or, 8, row); the low value is 47 (7 is the first "leaf" in the top, or, 4, row). The difference is , which is the range.

Quantity A: The median (middle number) is , and the mode (most common number) is , so the sum of the two numbers is .

Quantity B: The range is the smallest number subtracted from the largest number, which is .

Quantity A is larger.

The median is the average of the two middle values of a set of data with an even number of values. So we have:

The range is the difference between the lowest and the highest values. So we have:

So the range is greater than the median.

The mean of a set of data is given by the sum of the data, divided by the total number of values in the set. So we can write:

The range is the difference between the lowest and the highest values. So we have:

So the mean is greater than the range.

The mode of a set of data is the value which occurs most frequently which is  in this problem.

The range is the difference between the lowest and the highest values. So we have:

So the range is equal to the mode.

The mean of a set of data is given by the sum of the data, divided by the total number of values in the set. So we can write:

The median is the average of the two middle values of a set of data with an even number of values. So we have:

So we have:

The range is the difference between the lowest and the highest values. So we have:

Therefore is greater than .

If 60% of the students are boys, 40% are girls (100 – 60 = 40). Multiply 25 by 40% (25 * 0.4 = 10); therefore, 10 students are girls.

The sets are divided according to the remainder obtained when each element is divided by 4. 197 divided by 4 yields a remainder of 1; all of the elements of  match this description, so .