Mean, Median, and Mode - ISEE Middle Level Mathematics Achievement

1. What is the mode of a data set?

   The value that occurs most often. The mode identifies the data value with the highest frequency of occurrence in the set.

2. Identify the mode of the numbers $5,5,6,6,7,7$.

   No mode. Since all values appear with equal frequency, there is no unique mode in the set.

3. What two positions are averaged to find the median when $n$ is even and the list is ordered?

   Positions $\frac{n}{2}$ and $\left(\frac{n}{2}\right)+1$. These positions locate the two central values whose average gives the median for an even number of ordered values.

4. What is the mean of the numbers $3,3,3,9$?

   $4.5$. Sum $3+3+3+9=18$ and divide by $4$ to find the average of the set.

5. What is the mean of the numbers $10,12,14$?

   $12$. Sum $10+12+14=36$ and divide by $3$ to compute the average value.

6. What is the median of the numbers $-3,-1,-2,-4,-5$?

   $-3$. In the ordered list $-5,-4,-3,-2,-1$, the median is the third value for odd $n$.

7. Which option is the correct first step to find the median of $7,1,9,3,5,3$?

   Order the data from least to greatest. Ordering is necessary to identify the middle value(s) for calculating the median.

8. What is the mean of the numbers $1,2,2,5$?

   $2.5$. Sum $1+2+2+5=10$ and divide by $4$ to compute the average.

9. What is the median of the numbers $1,2,7,8,10,11$?

   $\frac{7+8}{2}=7.5$. With an even number of ordered values $1,2,7,8,10,11$, average the third and fourth to find the median.

10. What is the mean of the numbers $2,4,6,8$?

    $5$. Calculate the mean by summing $2+4+6+8=20$ and dividing by $4$ to get the average.

11. What is the median of a data set after the values are arranged from least to greatest?

    The middle value (or average of two middle values). The median is the central value in an ordered list, or the average of the two central values if the count is even.

12. What is the median position (index) for $n$ values when $n$ is odd and the list is ordered?

    $\frac{n+1}{2}$. This formula determines the position of the median in an ordered list with an odd number of values.

13. What is the median of the numbers $12,1,6,2$?

    $\frac{2+6}{2}=4$. Order as $1,2,6,12$ and average the second and third values for the even count median.

14. What is the median of the numbers $4,4,4,9,10$?

    $4$. In the ordered list $4,4,4,9,10$, the median is the third value for an odd count.

15. What is the mean of a data set with sum $48$ and $n=6$ values?

    $8$. Divide the total sum $48$ by the number of values $6$ to find the average.

16. What is the median of the numbers $9,2,7,5,3$?

    $5$. Order the numbers as $2,3,5,7,9$ and select the middle value for the median.

17. What is the mean of a data set in terms of sum $S$ and number of values $n$?

    $\text{mean}=\frac{S}{n}$. The mean represents the average value, obtained by dividing the total sum of the data points by the number of data points.

18. What is the median of the ordered set $2,3,3,5,7,9$?

    $\frac{3+5}{2}=4$. For even $n=6$, average the third and fourth values in the ordered set.

19. What is the mode of the numbers $0,1,1,2,2,3$?

    $1$ and $2$. Both $1$ and $2$ appear twice, the highest frequency, making the set bimodal.

20. What is the median of the numbers $6,2,9,2,1,2,8$?

    $2$. Order as $1,2,2,2,6,8,9$ and select the fourth value for odd $n=7$.

21. What is the median position for $n=9$ ordered values (give the index number)?

    $5$. Use $(9+1)/2=5$ to find the position of the median in an odd-numbered ordered list.

22. What is the mean of the numbers $20,25,30,35,40$?

    $30$. Sum $20+25+30+35+40=150$ and divide by $5$ to get the arithmetic average.

23. What is the mode of the numbers $8,9,10,11$?

    No mode. All values are unique with frequency one, so no value occurs most often.

24. What is the mode of the numbers $1,3,3,4,4,4,6$?

    $4$. The mode is the value $4$, which appears three times, more frequently than others.

25. What is the mean of the numbers $-2,-1,0,1,2$?

    $0$. The sum is $0$, so dividing by $5$ yields the average of symmetric positive and negative values.

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