Airport Parking The number of short-term parking spaces at 15 airports is shown. Find the mean, median, mode, and midrange for the data. 750 3400 1962 700 203 900 8662 260 1479 5905 9239 690 9822 1131 2516
The Correct Answer and Explanation is:
To analyze the data:
750, 3400, 1962, 700, 203, 900, 8662, 260, 1479, 5905, 9239, 690, 9822, 1131, 2516
We will find the mean, median, mode, and midrange.
Step 1: Organize the Data in Ascending Order
203, 260, 690, 700, 750, 900, 1131, 1479, 1962, 2516, 3400, 5905, 8662, 9239, 9822
Mean
Add all the numbers, then divide by the total count (15):
Sum =
203 + 260 + 690 + 700 + 750 + 900 + 1131 + 1479 + 1962 + 2516 + 3400 + 5905 + 8662 + 9239 + 9822 = 54219
Mean = 54219 / 15 = 3614.6
Median
With 15 values, the median is the 8th value:
Median = 1479
Mode
The mode is the value(s) that appear most frequently.
Each value appears only once.
Mode = None (or No mode)
Midrange
Midrange = (Minimum + Maximum) ÷ 2
= (203 + 9822) ÷ 2 = 10025 ÷ 2 = 5012.5
Final Answers
- Mean: 3614.6
- Median: 1479
- Mode: No mode
- Midrange: 5012.5
Explanation
In statistics, measures of central tendency and position help us understand the distribution of a dataset. This problem involves analyzing the number of short-term parking spaces at 15 different airports using four common metrics: mean, median, mode, and midrange.
The mean is the arithmetic average. We calculate it by adding all the values and dividing by how many values there are. In this case, the sum of all parking space counts is 54219, and there are 15 values, so the mean is 3614.6. The mean is affected by very large or small values, so the high numbers such as 9822 and 9239 have pulled the average up.
The median is the middle value when the data is ordered from smallest to largest. Since there are 15 numbers, the 8th number in the ordered list is the median. This is 1479. The median gives a better idea of the “typical” value when data is skewed because it is not influenced by outliers.
The mode refers to the number that occurs most frequently. Here, each value occurs only once. Therefore, there is no mode in this dataset. This tells us there is no most common number of short-term parking spaces among the airports.
The midrange is calculated by averaging the smallest and largest values. The smallest is 203 and the largest is 9822, so the midrange is 5012.5. Like the mean, the midrange is influenced by extreme values and gives a sense of the center based on the range.
In summary, these different measures provide a broader understanding of the distribution. The mean and midrange are both higher than the median, indicating the data is right-skewed due to some airports having very large numbers of parking spaces.
