Airport Parking: Mean, Median, Mode, And Midrange Explained

by Alex Johnson 60 views

Welcome! Today, we're diving into a real-world scenario involving airport parking data. We've got the number of short-term parking spaces at eight different airports, and our goal is to figure out the mean, median, mode, and midrange of this dataset. These statistical measures help us understand the central tendency and spread of our data, giving us a clearer picture of typical parking availability. Let's break down each of these concepts and apply them to our specific numbers.

Understanding the Data

First, let's list out the data we're working with. The number of short-term parking spaces at 8 airports are: 4585, 4666, 8213, 1771, 2796, 848, 6599, and 2826. Before we start calculating, it's always a good practice to arrange the data in ascending order. This makes it much easier to find the median and midrange. So, let's sort our numbers:

848, 1771, 2796, 2826, 4585, 4666, 6599, 8213

This sorted list will be our foundation for all the calculations to come. Each of these numbers represents the capacity of short-term parking at a specific airport. By analyzing these values, we can gain insights into the general scale of parking facilities airports provide for their short-term visitors. For instance, is there a typical number of spaces, or does it vary wildly? These statistics will help us answer that.

Calculating the Mean (Average)

Let's kick things off with the mean, which is probably the most familiar statistical measure – it's simply the average. To find the mean, you add up all the numbers in your dataset and then divide by the total count of numbers. In our case, we have 8 numbers representing the parking spaces.

So, first, we sum all the parking space counts:

4585 + 4666 + 8213 + 1771 + 2796 + 848 + 6599 + 2826 = 32304

Now, we divide this sum by the number of airports, which is 8:

Mean = 32304 / 8 = 4038

Therefore, the mean number of short-term parking spaces across these 8 airports is 4038. This average gives us a single value that summarizes the central tendency of the parking capacities. It suggests that, on average, an airport in this group has around 4038 short-term parking spots. However, it's important to remember that the mean can sometimes be skewed by very high or very low values (outliers), so let's explore other measures to get a more complete picture.

Finding the Median (Middle Value)

The median is another crucial measure of central tendency. It represents the middle value in a dataset when the data is arranged in ascending or descending order. The beauty of the median is that it's not affected by extreme outliers, making it a robust indicator, especially when dealing with potentially skewed data like parking space counts which can sometimes have airports with exceptionally large or small facilities. To find the median, we first need our sorted list of parking spaces:

848, 1771, 2796, 2826, 4585, 4666, 6599, 8213

Since we have an even number of data points (8 in this case), the median is calculated by taking the average of the two middle numbers. In our sorted list, the two middle numbers are the 4th and 5th values, which are 2826 and 4585.

To find the median, we add these two numbers and divide by 2:

Median = (2826 + 4585) / 2 Median = 7411 / 2 Median = 3705.5

So, the median number of short-term parking spaces for these airports is 3705.5. This means that half of the airports have fewer than 3705.5 parking spaces, and the other half have more. Comparing this to the mean (4038), we see a difference. The median is slightly lower, which might suggest that the higher values (like 8213) are pulling the mean up a bit. The median gives us a more balanced view of the typical airport parking capacity, unaffected by the largest facilities.

Identifying the Mode (Most Frequent Value)

The mode is the value that appears most frequently in a dataset. It tells us which specific number of parking spaces is most common among the airports surveyed. This can be very useful for understanding common practices or standard offerings. Let's look at our sorted list of parking spaces again:

848, 1771, 2796, 2826, 4585, 4666, 6599, 8213

When we examine this list, we notice that every single number is unique. None of the parking space counts are repeated. In such a situation, we say that the dataset has no mode. This indicates that there isn't one particular number of short-term parking spaces that occurs more often than any other within this specific group of 8 airports. It suggests a wide variety of parking capacities rather than a common standard among these particular airports. If, for example, two airports had 4585 spaces, then 4585 would be the mode. But here, each airport has a distinct number of spaces in our sample.

Determining the Midrange (Range Extremes)

Finally, let's calculate the midrange. The midrange is a simple measure that gives us the midpoint between the lowest and highest values in the dataset. It's calculated by adding the minimum and maximum values and then dividing by 2. The midrange gives us an idea of the center of the range of the data.

From our sorted list:

848, 1771, 2796, 2826, 4585, 4666, 6599, 8213

The minimum value (the smallest number of parking spaces) is 848. The maximum value (the largest number of parking spaces) is 8213.

Now, let's calculate the midrange:

Midrange = (Minimum Value + Maximum Value) / 2 Midrange = (848 + 8213) / 2 Midrange = 9061 / 2 Midrange = 4530.5

So, the midrange of the short-term parking spaces for these airports is 4530.5. This value represents the exact center point between the smallest and largest parking capacities in our dataset. It's a very straightforward measure but can be heavily influenced by the extreme values, just like the mean.

Summary of Findings

Let's recap what we've found for the number of short-term parking spaces at these 8 airports:

  • Mean: 4038
  • Median: 3705.5
  • Mode: No mode
  • Midrange: 4530.5

These statistics provide different perspectives on the distribution of parking spaces. The mean and midrange are pulled higher by the larger airport capacities, while the median offers a more central value unaffected by these extremes. The absence of a mode highlights the diversity in parking infrastructure among these particular airports. Understanding these measures helps us interpret data more effectively and draw meaningful conclusions.

For further reading on statistical measures and their applications, you can explore resources like Wikipedia's page on the Mean or delve into the educational content provided by Khan Academy's statistics section. These platforms offer comprehensive explanations and further examples to deepen your understanding of statistics in various contexts.