Question

twelve people were surveyed and asked how many people live in their residence. the results are summarized in the table below.

people per residence	frequency
2	4
3	3
4	1
5	1
6	1

what is the median number of people per residence? round to one decimal place if needed.

the median is 2 people per residence.
the median is 2.5 people per residence.
the median is 2.8 people per residence.
the median is 3.5 people per residence.

Explanation:

Step1: Calculate cumulative frequency

People per Residence	Frequency	Cumulative Frequency
2	4	2 + 4=6
3	3	6+3 = 9
4	1	9 + 1=10
5	1	10+1 = 11
6	1	11+1 = 12

The total number of data - points $n = 12$ (an even number).

Step2: Determine the median position

For a data - set with $n$ data - points (where $n$ is even), the median is the average of the values at positions $\frac{n}{2}$ and $\frac{n}{2}+1$ when the data is arranged in ascending order. Here, $\frac{n}{2}=\frac{12}{2}=6$ and $\frac{n}{2}+1 = 7$.

Step3: Find the values at the median positions

The 6th value falls within the "2 people per residence" category (since the cumulative frequency up to "2 people per residence" is 6). The 7th value falls within the "3 people per residence" category (as the cumulative frequency up to "2 people per residence" is 6 and up to "3 people per residence" is 9).

Step4: Calculate the median

Median=$\frac{2 + 3}{2}=2.5$

Answer:

The median is 2.5 people per residence.