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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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