Analyzing Train Data for Vacant Seats Calculation

This question asks us to calculate the average number of vacant seats across all the trains listed in the provided table. To do this, we first need to determine the number of vacant seats for each train and then find their average.

Understanding the Train Data Table

The table contains detailed information about five different trains (Train Number 1001, 1002, 1003, 1004, and 1005). The columns provide various details, including the total number of seats and the number of reserved seats for each train.

Calculating Vacant Seats for Each Train

The number of vacant seats for any train is the difference between the total number of seats and the number of reserved seats. We can calculate this for each train:

• Train 1001: Total Seats - Reserved Seats = 680 - 400 = 280 vacant seats
• Train 1002: Total Seats - Reserved Seats = 870 - 550 = 320 vacant seats
• Train 1003: Total Seats - Reserved Seats = 650 - 350 = 300 vacant seats
• Train 1004: Total Seats - Reserved Seats = 980 - 620 = 360 vacant seats
• Train 1005: Total Seats - Reserved Seats = 780 - 520 = 260 vacant seats

Finding the Total Vacant Seats

Now, we need to find the sum of the vacant seats for all five trains:

Total Vacant Seats = Vacant Seats (1001) + Vacant Seats (1002) + Vacant Seats (1003) + Vacant Seats (1004) + Vacant Seats (1005)

Total Vacant Seats = 280 + 320 + 300 + 360 + 260

Let's add these numbers: \( 280 + 320 = 600 \) \( 600 + 300 = 900 \) \( 900 + 360 = 1260 \) \( 1260 + 260 = 1520 \)

So, the total number of vacant seats across all trains is 1520.

Calculating the Average Number of Vacant Seats

To find the average, we divide the total number of vacant seats by the number of trains. There are 5 trains.

Average Vacant Seats = \( \frac{\text{Total Vacant Seats}}{\text{Number of Trains}} \)

Average Vacant Seats = \( \frac{1520}{5} \)

Let's perform the division: \( 1520 \div 5 = 304 \)

The average number of vacant seats for all trains is 304.

Conclusion on Train Vacant Seats Average

Based on our calculations using the train data table, the average number of vacant seats is 304. This aligns with one of the provided options.

Revision Table: Key Calculations for Train Data

Here's a summary of the vacant seats calculation for each train and the final average.

Average Vacant Seats = \( \frac{1520}{5} = 304 \)

Additional Information on Data Analysis and Averages

Calculating averages is a fundamental concept in data analysis. The average (or mean) gives us a central value for a set of numbers.

• Mean: The sum of all values divided by the number of values. This is what we calculated here.
• Median: The middle value in a dataset that is ordered from least to greatest.
• Mode: The value that appears most frequently in a dataset.

In this specific problem about train vacant seats, calculating the mean average helps understand the typical number of empty seats across the different train services. This type of data analysis is useful for planning and optimization in transportation or other industries dealing with capacity and occupancy.