Lesson 15: Estimating Population Measures of Center | Unit 8: Probability and Sampling

A random sample of 15 items are selected. For this data set, is the mean or median a better measure of center? Explain your reasoning.

Han and Priya want to know the mean height of the 30 students in their dance class. They each select a random sample of 5 students. The mean height for Han’s sample is 59 inches. The mean height for Priya’s sample is 61 inches. Does it surprise you that the two sample means are different? Explain your reasoning.

Han and Priya want to know the mean height of the 30 students in their dance class. They each select a random sample of 5 students. The mean height for Han’s sample is 59 inches. The mean height for Priya’s sample is 61 inches. Are the population means different? Explain your reasoning.

Clare and Priya each took a random sample of 25 students at their school. Clare asked each student in her sample how much time they spend doing homework each night. The sample mean is 1.2 hours, and the MAD is 0.6 hours. Priya asked each student in her sample how much time they spend watching TV each night. The sample mean is 2 hours, and the MAD is 1.3 hours. At their school, do you think there is more variability in how much time students spend doing homework or watching TV? Explain your reasoning.

Clare and Priya each took a random sample of 25 students at their school. Clare estimates the students at her school spend an average of 1.2 hours each night doing homework. Priya estimates the students at her school spend an average of 2 hours each night watching TV. Which of these two estimates is likely to be closer to the actual mean value for all the students at their school? Explain your reasoning.

Clare and Priya each took a random sample of 25 students at their school. Clare estimates the students at her school spend an average of 1.2 hours each night doing homework. Priya estimates the students at her school spend an average of 2 hours each night watching TV. Which of these two estimates is likely to be closer to the actual mean value for all the students at their school? Explain your reasoning.

The science teacher gives daily homework. For a random sample of days throughout the year, the median number of problems is 5, and the IQR is 2. The Spanish teacher also gives daily homework. For a random sample of days throughout the year, the median number of problems is 10, and the IQR is 1. If you estimate the median number of science homework problems to be 5 and the median number of Spanish problems to be 10, which is more likely to be accurate? Explain your reasoning.