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The number of cars per apartment, owned by a sample of tenants in a large complex, is \(1,2,1,2,2,2,1,2,3,2 .\) What is the mode?

Short Answer

Expert verified
The mode is 2.

Step by step solution

01

Interpret the data set

The data set given is the number of cars per apartment owned by tenants in a large complex. The numbers represented are \(1,2,1,2,2,2,1,2,3,2\). This means, for instance, that one tenant owns 1 car, another owns 2 cars, and so on.
02

Count the occurrences

To find the mode, it is necessary to count how many times each number appears in the data set. Doing this, the 1 appears 3 times, the 2 appears 6 times, and the 3 appears only once.
03

Determine the mode

The mode is the number that appears the most. According to the counts, the number 2 appears the most in this data set. Therefore, the mode of this data set is 2.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding a Data Set
A data set is a collection of related numbers or values that represent information about a topic. When analyzing a data set, it's essential to understand what the numbers signify. In the given exercise, the data set is a sequence of numbers representing the number of cars each tenant owns in an apartment complex. Each number corresponds to an apartment, telling us how many cars belong to the people living there. Looking at the data set, you can observe trends, such as finding out the most common number of cars owned by the tenants, which is precisely what determining the mode achieves. By examining the list of numbers, we gain insights into the living arrangements and car occupancy at the apartment complex, which could be useful for resource planning or other assessments.
Frequency: How Often Things Happen
Frequency refers to the number of times a particular value appears in a data set. Calculating frequency is crucial for identifying features like the mode of the data set. In this specific example, we count how many times each number of cars appears among the tenants.

  • 1 car is owned by 3 tenants.
  • 2 cars are owned by 6 tenants.
  • 3 cars are owned by 1 tenant.

The value with the highest frequency is the mode of the data set. In our case, since the number 2 appears most frequently, it is the mode. Understanding frequency helps us grasp how common or rare certain values are within a set, highlighting the nature of the data set at a glance.
Counting the Number of Cars
In this exercise, the focus is on counting the number of cars owned by tenants in the apartment complex. Each number in the data set represents a certain number of cars per apartment. To find the mode, one must tally the occurrences of each number.

  • The number 1 appears 3 times.
  • The number 2 shows up 6 times.
  • The number 3 is present just once.

The most frequently occurring number gives us the mode, which, in this case, is 2. Counting the number of cars not only determines the mode but also provides a complete picture of car distribution within the complex. This knowledge can aid in decision-making processes, such as improving parking facilities to accommodate the most common number of vehicles.
Living in an Apartment Complex
An apartment complex is a group of apartment buildings managed collectively, containing multiple housing units. When observing data from such settings, it's essential to consider the communal living environment, where resources and facilities are shared among many apartments.

In our scenario, focusing on the number of cars per apartment helps understand residents' transportation needs. Often in apartment complexes, data like the number of cars per unit can assist in planning shared resources, like parking space availability. If all tenants owned multiple cars, it might signify a need for more parking spaces, or if few cars are owned, suggesting alternative transport options, like public transit or shared vehicle systems, could be promoted. Thus, data and mode analysis in the context of an apartment complex yields practical insights into residents' lifestyle and communal requirements.

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