A survey groups 10 students by weekly study hours: 2 students in the interval 0 to 2 hours, 5 students in 2 to 4 hours, and 3 students in 4 to 6 hours. Using interval midpoints, what is the best estimate of the mean study time?

1. With grouped data the individual values are unknown, so each interval is represented by its midpoint. 2. The midpoints are 1 hour, 3 hours, and 5 hours for the three intervals. 3. Multiply each midpoint by its frequency: 2 x 1 = 2, 5 x 3 = 15, 3 x 5 = 15. 4. Add the products: 2 + 15 + 15 = 32 student-hours. 5. Divide by the total frequency: 32 / 10 = 3.2 hours. 6. So the best estimate of the mean is 3.2 hours of study per week. 7. Option B, 3.0, simply averages the three midpoints and ignores how many students sit in each interval. 8. Option C divides by 11 and option D weights the top interval double, both breaking the frequency table method. _Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.3 Measures of the Center of the Data_