- Identify the total population: 4,000 students.
- Identify the percentage for the category "50-100": 75%.
- Convert the percentage to decimal: \(0.75\).
- Calculate the total number of students: \(4,000 \times 0.75 = \boxed{3000}\).
Explanation
- Problem Analysis
We are given that a total of 4,000 students were surveyed about their daily text messaging habits. The survey results are provided in a frequency table indicating the percentage of students in different categories of text messages sent per day. We are interested in the specific category of "50-100" text messages, which corresponds to 75% of the total number of students surveyed. Our objective is to determine the absolute number of students who reported sending between 50 and 100 text messages per day.
- Conversion of Percentage to Decimal
To find the number of students in the 50-100 category, we need to calculate 75% of the total number of students. The total number of students is 4,000. The percentage of students in the desired category is 75%. To use this percentage in a calculation, we convert it to a decimal by dividing by 100:
\[75\% = \frac{75}{100} = 0.75\]
- Calculation of the Final Result
Now, we multiply the total number of students by the decimal form of the percentage to find the number of students who send 50-100 texts per day:
\[\text{Number of students} = 4,000 \times 0.75\]
Performing this calculation:
\[4,000 \times 0.75 = 3,000\]
Thus, 3,000 students reported sending 50-100 text messages per day.
Examples
Understanding how to calculate portions of a total population using percentages is a fundamental skill used in many real-world situations. For example, if a store owner wants to know how many of their 5,000 customers prefer a certain brand of sneakers, they might use data showing that 40% of their customer base buys that brand. By calculating \(5,000 \times 0.40 = 2,000\), the owner determines that 2,000 customers favor those sneakers, which helps them effectively manage their inventory and plan marketing strategies. This skill is essential for data analysis, resource management, and making informed decisions in various professional and personal contexts.