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

1. What is the range of the data set $\{0,0,0,5\}$?

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

2. What is the range of the data set $\{\frac{1}{2},\frac{3}{2},2,\frac{5}{2}\}$?

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

3. What is the range of the data set $\{12,15,11,13,14\}$?

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

4. What is the mode of the data set $\{7,8,9\}$?

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

5. What is the median of the ordered data set $\{2,2,2,2,9\}$?

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

6. What is the median of a data set with an even number of values after the values are ordered?

   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.

7. What is the median of the ordered data set $\{1,3,3,7,9,9\}$?

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

8. What is the range of the data set $\{-3,-1,-7,2\}$?

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

9. What is the range of a data set in terms of its maximum and minimum values?

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

10. What is the mode of the data set $\{5,5,6,6,7,7\}$?

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

11. What is the median of the ordered data set $\{2,5,8,11\}$?

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

12. What is the range of the data set $\{3,7,7,2,10\}$?

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

13. What is the median of the data set $\{8,3,5,3,10\}$?

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

14. What is the mode of the data set $\{1,2,2,3,3,3,4\}$?

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

15. What is the mode of a data set?

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

16. What is the mode of the data set $\{\frac{1}{3},\frac{1}{3},\frac{1}{2},\frac{2}{3}\}$?

    $\frac{1}{3}$. $\frac{1}{3}$ appears twice, more frequently than the other distinct values.

17. What is the median of the ordered data set $\{-5,-2,0,4,9,12\}$?

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

18. What is the median of a data set with an odd number of values after the values are ordered?

    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.

19. What is the range of the data set $\{-10,-10,-2,-3\}$?

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

20. What is the mode of the data set $\{2,2,3,3,5\}$?

    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.

21. What is the mode of the data set $\{4,1,4,2,4,3\}$?

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

22. What is the median of the data set $\{0,1,1,2,100\}$?

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

23. What is the median of the ordered data set $\{1,4,6,9,12\}$?

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

24. What is the median of the data set $\{6,1,9,2,8,3\}$?

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

25. What is the median of the ordered data set $\{\frac{1}{4},\frac{1}{2},\frac{3}{4},1\}$?

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

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