Finding the Average Number of Admitted Students

The question asks for the average number of students admitted in specific colleges during specific years: College A in 2015, College B in 2016, and College C in 2019. To find the average, we need to identify the number of students admitted in each of these instances from the provided table, sum these numbers, and then divide the sum by the count of instances (which is 3).

Step-by-Step Calculation

Let's identify the number of admitted students for each required case from the table:

• Number of students admitted in College A in the year 2015: From the table, locate the row for year 2015 and the column for College A. The value is 15000.
• Number of students admitted in College B in the year 2016: From the table, locate the row for year 2016 and the column for College B. The value is 23000.
• Number of students admitted in College C in the year 2019: From the table, locate the row for year 2019 and the column for College C. The value is 16000.

Next, we sum these values:

Sum = (Students in College A, 2015) + (Students in College B, 2016) + (Students in College C, 2019)

Sum = \(15000 + 23000 + 16000\)

Sum = \(54000\)

Now, we calculate the average by dividing the sum by the number of instances (which is 3):

Average = \(\frac{\text{Sum}}{\text{Number of instances}}\)

Average = \(\frac{54000}{3}\)

Average = \(18000\)

Therefore, the average number of students admitted in college A in the year 2015, in college B in the year 2016, and in college C in the year 2019 together is 18000.

Conclusion

Based on the data from the table and the calculation, the average number of students for the specified college-year combinations is 18000.

Revision Table - Data Interpretation

This table summarizes the key data points used in the calculation:

Additional Information - Calculating Averages

Calculating an average is a fundamental concept in mathematics and data analysis. Here's a brief explanation:

• What is an Average? The average (or arithmetic mean) is a single value that represents the central tendency of a set of numbers. It's calculated by summing all the numbers in the set and then dividing by the count of numbers in the set.
• Formula: The formula for the arithmetic mean (\(\bar{x}\)) of a set of numbers (\(x_1, x_2, \dots, x_n\)) is:

  \(\bar{x} = \frac{x_1 + x_2 + \dots + x_n}{n} = \frac{\sum_{i=1}^{n} x_i}{n}\)

  Where:

  • \(\sum x_i\) is the sum of all the numbers in the set.
  • \(n\) is the total count of numbers in the set.
• Usefulness: Averages are useful for understanding typical values, comparing different sets of data, and identifying trends. In data interpretation problems like this, calculating averages helps summarize specific aspects of the data presented in tables or charts.