Range, Median, and Mode - ISEE Upper Level: Mathematics Achievement

$1$. Ordered as $0,1,1,2,100$, the median is the third value $1$ in this odd set.

$8$. Ordered as $-10,-10,-3,-2$, subtract minimum $-10$ from maximum $-2$ to get the range.

No mode (three values tie for most frequent). Since $5,6,7$ each appear twice and no value more, there is no unique mode.

$5$. For this six-element ordered set, average the third and fourth values: $(3+7)/2 = 5$.

$9$. Ordered as $-7,-3,-1,2$, the range is the difference between maximum $2$ and minimum $-7$.

$5$. Ordered as $3,3,5,8,10$, the median is the middle value $5$ in this odd-numbered set.

$4$. In the set, $4$ appears three times, more frequently than any other value.

$\frac{13}{2}$. For this four-element ordered set, average the second and third values: $(5+8)/2 = 13/2$.

$4$. Ordered as $11,12,13,14,15$, the range is the maximum $15$ minus the minimum $11$.

$2$. In this five-element ordered set, the median is the third value, which is $2$.

No mode (all values occur once). All values in the set appear exactly once, resulting in no mode.

$5$. The range is the difference between the maximum $5$ and the minimum $0$ in the set.

$\frac{9}{2}$. Ordered as $1,2,3,6,8,9$, average the third and fourth values: $(3+6)/2 = 9/2$.

$\frac{5}{8}$. For this four-element ordered set, average the second and third: $(\frac{1}{2} + \frac{3}{4})/2 = \frac{5}{8}$.

$2$. Ordered as $\frac{1}{2},\frac{3}{2},2,\frac{5}{2}$, subtract minimum $\frac{1}{2}$ from maximum $\frac{5}{2}$.

$2$. For this six-element ordered set, average the third and fourth values: $(0+4)/2 = 2$.

No mode (two values tie for most frequent). Since $2$ and $3$ each appear twice and no value appears more, there is no unique mode.

$6$. In this five-element ordered set, the median is the third value, which is $6$.

$8$. After ordering the set as $2,3,7,7,10$, subtract the minimum $2$ from the maximum $10$ to find the range.

The value that occurs most often. The mode identifies the most frequently occurring value within the data set.

The average of the two middle values. For an even number of ordered values, the median is calculated as the arithmetic mean of the two central numbers.

$3$. In the set, $3$ appears three times, which is more frequent than any other value.

The middle value in the ordered list. In an ordered data set with an odd number of elements, the median is the central value positioned at the middle.

$\text{range}=\text{max}-\text{min}$. The range quantifies the spread of data by subtracting the minimum value from the maximum value in the set.