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 |
| :------------------- | :-------- |
| 1 | 2 |
| 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.
A. The median is 2 people per residence.
B. The median is 2.5 people per residence.
C. The median is 2.8 people per residence.
D. The median is 3.5 people per residence.
Answer (2)
List the data in ascending order based on frequency.
Identify the 6th and 7th values since there are 12 data points.
Calculate the median by averaging the 6th and 7th values: 2 2 + 3 = 2.5 .
The median number of people per residence is 2.5 .
Explanation
Understand the problem and provided data We are given a frequency table that shows the number of people per residence from a survey of twelve people. Our goal is to find the median number of people per residence. The median is the middle value when the data is arranged in ascending order.
List the data in ascending order First, we list the number of people per residence in ascending order, according to their frequency: 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 5, 6
Identify the middle values Since there are 12 data points (an even number), the median is the average of the 6th and 7th values. The 6th value is 2 and the 7th value is 3.
Calculate the median Now, we calculate the median by averaging the 6th and 7th values: 2 2 + 3 = 2 5 = 2.5
State the final answer Therefore, the median number of people per residence is 2.5.
Examples
Understanding the median number of people per residence can help urban planners and policymakers make informed decisions about housing and resource allocation. For example, if the median household size is increasing, there might be a need for more family-sized housing units and larger infrastructure to support the growing population. This measure provides a central value that represents the typical household size in a community, offering valuable insights for planning and development.
The median number of people per residence is 2.5, calculated by averaging the 6th and 7th values from the ordered data. This places the answer in option B. This median value reflects the central tendency of household sizes in the survey.
;
