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Charolette is looking for a 3-bedroom apartment with 2 bathrooms. The rents of six different apartments from the local area are listed below in dollars per month. Find the median. Apartment 1: \( \$ 1650 \) Apartment 2: \( \$ 1700 \) Apartment 3: \( \$ 2050 \) Apartment 4: \( \$ 2100 \) Apartment 5: \( \$ 1750 \) Apartment 6: \( \$ 2400 \) \$ \$2050 \$ \$1900 \$2075

Ask by Colon Hodges. in the United States
Nov 07,2024

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Tutor-Verified Answer

Answer

The median rent is \( \$ 1900 \).

Solution

To find the median of the given apartment rents, we first need to arrange the rents in ascending order. Then, we can determine the median based on the number of data points. Here are the rents in ascending order: Apartment 1: \( \$ 1650 \) Apartment 2: \( \$ 1700 \) Apartment 3: \( \$ 1750 \) Apartment 4: \( \$ 2050 \) Apartment 5: \( \$ 2100 \) Apartment 6: \( \$ 2400 \) Since there are 6 apartments (an even number of data points), the median will be the average of the two middle numbers. The two middle numbers are the 3rd and 4th numbers in the ordered list: Apartment 3: \( \$ 1750 \) Apartment 4: \( \$ 2050 \) Now, we find the average of these two numbers: Median = \( \frac{1750 + 2050}{2} \) Median = \( \frac{3800}{2} \) Median = \( \$ 1900 \) So, the median rent for the apartments is \( \$ 1900 \).

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The Deep Dive

To find the median rent for Charolette's apartment search, first, we need to arrange the rents in ascending order: - \( \$ 1650 \) - \( \$ 1700 \) - \( \$ 1750 \) - \( \$ 2050 \) - \( \$ 2100 \) - \( \$ 2400 \) Since there are six rents (an even number), the median will be the average of the two middle values. In this case, the two middle values are \( \$ 1750 \) and \( \$ 2050 \). Calculating the median: \( \text{Median} = \frac{\$ 1750 + \$ 2050}{2} = \frac{\$ 3800}{2} = \$ 1900 \) So, the median rent is \( \$ 1900 \). --- When it comes to apartment hunting, knowing the median rent is powerful. It gives Charolette a clear insight into what a typical rent looks like, avoiding any potential bias from extremely high or low rents. This way, she can better negotiate or manage her budget based on realistic figures. Moreover, a common mistake when calculating the median is to overlook that it should reflect the middle value of a properly ordered list. Always double-check that the numbers are sorted before making your calculations. It's like having a tidy home—organized and ready for visitors (or in this case, potential renters)!

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