Maximum of 16 students. How many students are the median and average?

Understand the Problem

The question is asking for the median and average number of students, within the context of a maximum of 16 students. This implies we need to determine how these statistical measures apply to a group of students with the specified limitation.

Answer

Average: $12.57$, Median: $13$.

Steps to Solve

Gather Data on Number of Students

Assuming we have a list of student counts across various groups, we first need to collect this data. For example, let's say the counts are: $$ [12, 15, 10, 8, 13, 16, 14] $$

Calculate the Average (Mean) Number of Students

To find the average:

Sum all the counts of students.
Divide by the total number of groups.

For our example: $$ \text{Total Sum} = 12 + 15 + 10 + 8 + 13 + 16 + 14 = 88 $$

There are 7 groups (7 counts).

Now, calculate the average: $$ \text{Average} = \frac{88}{7} \approx 12.57 $$

Calculate the Median Number of Students

To find the median:

Sort the data in ascending order: $$ [8, 10, 12, 13, 14, 15, 16] $$
Since there are 7 values (an odd number), the median is the middle value. The fourth number in this sorted list is 13.

Recap the Values

Average number of students: approximately 12.57
Median number of students: 13

The average number of students is approximately $12.57$, and the median number of students is $13$.

More Information

The average provides insight into the overall distribution of students, while the median offers information about the middle point of the data. Both are essential for analyzing group sizes effectively.

Tips

Forgetting to sort the data when calculating the median.
Not correctly dividing the sum of students by the total number of groups for the average.
Confusing median and average; they represent different statistical measures.

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