Relative Frequencies Worksheets Grade 11

1. Noah surveyed 220 Grade 11 students about their preferred method of study. 143 students indicated they prefer studying in groups. What is the relative frequency of students who prefer group study, and what does this value mean in the context of the survey?
2. Kaia surveyed 231 Grade 11 students about their preferred method of studying for exams. 77 students preferred group study sessions. What is the relative frequency of students who prefer group study, and what does this value mean in context?
3. A marine biologist is studying the population dynamics of a dolphin pod. She observes that the relative frequency of juvenile dolphins in the pod is 0.28. If the total pod size is 75 dolphins, and the biologist wants to estimate how many dolphins would be juveniles in a larger population of 500 dolphins from the same ecosystem, what is her best estimate based on this relative frequency?

…and 4 more problems

1. Isabella is analyzing the results of a survey at her school about participation in extracurricular activities. She collected data from 320 students and found that 84 of them participate in at least two extracurricular activities. What is the relative frequency of students who participate in at least two extracurricular activities? Interpret this relative frequency in the context of the school's student body of 1,200 students.
2. A Ferris wheel with a diameter of 40 meters completes one full rotation every 2 minutes. The height of a passenger above the ground, in meters, can be modeled by the function h(t) = 20 + 20sin(πt + φ), where t is time in minutes. If a passenger boards at the lowest point, which is 5 meters above the ground, determine the exact value of φ and the time when the passenger first reaches a height of 35 meters during the ride.
3. Noah surveyed 255 Grade 11 students about their preferred method of learning mathematics: 102 chose visual aids. Calculate the relative frequency of students who prefer visual aids and interpret what this value means in the context of the survey.

…and 4 more problems

1. A regular hexagon is inscribed in a circle with radius 10 cm. The hexagon is divided into 6 congruent equilateral triangles by drawing lines from the center to each vertex. If one of these triangles is rotated 60 degrees clockwise about the center of the circle, and then reflected across a line through the center and one vertex, describe the final position of the triangle relative to its original position and calculate the area of the overlapping region between the original and transformed triangles.
2. Mere is analyzing a two-way table from a survey of 800 high school students, comparing whether they participate in extracurricular sports and their academic performance. The table shows that 240 students both participate in sports and have a GPA above 3.0. The relative frequency of students who participate in sports among those with a GPA above 3.0 is 0.60. Based on this relative frequency, what does this value indicate about the relationship between sports participation and high academic performance in this survey context?
3. A wildlife biologist is studying the population growth of an endangered species. The population P(t) after t years is modeled by the function P(t) = 500e^(0.03t). If the current population is 500 individuals, how many years will it take for the population to reach 750 individuals? Round your answer to the nearest tenth of a year.

…and 2 more problems