Finding the Mode - ISEE Lower Level Mathematics Achievement

1. What is the mode of the data set $4, 4, 4, 4, 7, 7, 9$?

   $4$. $4$ appears four times, far exceeding $7$ (twice) and $9$ (once).

2. What is the mode of the data set $1.5, 2.0, 1.5, 3.0$?

   $1.5$. $1.5$ appears twice, while $2.0$ and $3.0$ each appear once.

3. What is the mode of a data set?

   The value that occurs most often in the data set. The mode identifies the most frequently appearing value, providing insight into the central tendency of categorical or discrete data.

4. What does it mean if a data set has no mode?

   No value occurs more often than all others. When all values appear with equal frequency, typically once, no single value stands out as occurring most often.

5. What does it mean if a data set is bimodal?

   It has exactly $2$ values tied for greatest frequency. Bimodal datasets feature two distinct values sharing the highest frequency, indicating two peaks in the data distribution.

6. What is the mode of the data set $3, 5, 5, 7, 9$?

   $5$. $5$ appears twice, more frequently than any other value in the set.

7. What is the mode of the data set $11, 12, 13, 11, 14, 15, 16$?

   $11$. $11$ appears twice, more frequently than any other value, each appearing once.

8. What is the mode of the data set $2, 4, 6, 8$?

   No mode. All values appear exactly once, resulting in equal frequencies and thus no mode.

9. What is the mode of the data set $10, 10, 10, 8, 8, 6$?

   $10$. $10$ appears three times, exceeding the frequencies of $8$ (twice) and $6$ (once).

10. What is the mode of the data set $0, 0, 1, 1, 1, 2$?

    $1$. $1$ appears three times, more than $0$ (twice) and $2$ (once).

11. What is the mode of the data set $2, 2, 2, 3, 3, 4, 4, 4$?

    $2$ and $4$. $2$ and $4$ each appear three times, tying for the highest frequency over $3$ (twice).

12. What is the mode of the data set $3, 3, 2, 2, 1, 1, 0$?

    $1$, $2$, and $3$. $1$, $2$, and $3$ each appear twice, sharing the maximum frequency, while $0$ appears once.

13. What is the mode of the data set $6, 6, 5, 5, 4, 4$?

    $4$, $5$, and $6$. $4$, $5$, and $6$ each appear twice, tying for the highest frequency.

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

    $\frac{1}{2}$. $\frac{1}{2}$ appears twice, exceeding the single appearances of $\frac{1}{3}$ and $\frac{1}{4}$.

15. What is the mode of the data set $12, 11, 12, 13, 11, 12$?

    $12$. $12$ appears three times, more than $11$ (twice) and $13$ (once).

16. Which value is the mode if $8$ occurs $3$ times, $9$ occurs $3$ times, and $10$ occurs $1$ time?

    $8$ and $9$. $8$ and $9$ both appear $3$ times, tying for the maximum frequency over $10$'s $1$.

17. What is the mode of the data set $5, 1, 5, 2, 3, 5, 2$?

    $5$. $5$ appears three times, more than $2$ (twice) and $1$ or $3$ (once each).

18. What is the mode of the data set $7, 8, 9, 7, 8, 9, 10$?

    $7$, $8$, and $9$. $7$, $8$, and $9$ each appear twice, sharing the maximum frequency over $10$ (once).

19. What is the mode of the data set $100, 90, 100, 80, 90, 70$?

    $90$ and $100$. $90$ and $100$ each appear twice, tying for the highest frequency over $80$ and $70$ (once each).

20. What is the mode of the data set $9, 7, 9, 7, 8, 7, 9$?

    $7$ and $9$. Both $7$ and $9$ appear three times, tying for the highest frequency, while $8$ appears once.

21. Identify the mode of the data set $14, 15, 14, 16, 17, 14, 15$.

    $14$. $14$ appears three times, exceeding $15$ (twice) and $16$ or $17$ (once each).

22. What is the mode of the data set $1, 2, 2, 3, 3, 4$?

    $2$ and $3$. Both $2$ and $3$ appear twice, tying for the highest frequency in the set.

23. Which value is the mode if $2$ occurs $5$ times and $3$ occurs $4$ times?

    $2$. $2$ has the highest frequency of $5$, compared to $3$'s $4$.

24. What does it mean if a data set is multimodal?

    It has more than $2$ values tied for greatest frequency. Multimodal datasets exhibit three or more values with the same maximum frequency, reflecting multiple peaks in the distribution.

25. What is the mode of the data set $-1, -1, -2, -2, -2, 0$?

    $-2$. $-2$ appears three times, surpassing $-1$ (twice) and $0$ (once).

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