# ﻿Comparing Populations Using Samples

Warmup

Without calculating, tell whether the pair of data sets have the same mean and whether they have the same mean absolute deviation.

Activity #1

`Practice ``Exercise Questions on Comparing Populations Samples. ` • Use the box plot samples below to answer the questions that follow.

When anthropologists find steel artifacts, they can test the amount of carbon in the steel to learn about the people that made the artifacts. Here are some box plots showing the percentage of carbon in samples of steel that were found in two different regions: (1.) Was there any steel found in region 1 that had more carbon than some of the steel found in region 2?

(2.) Was there any steel found in region 1 that had less carbon than some of the steel found in region 2?

(3.) Do you think there is a meaningful difference between all the steel artifacts found in regions 1 and 2?

(4.) Which sample has a distribution that is not approximately symmetric?

(5.) What is the difference between the sample medians for these two regions? (5.) Express the difference between these two sample medians as a multiple of the larger interquartile range.

(6.) The anthropologists who conducted the study concluded that there was a meaningful difference between the steel from these regions. Do you agree? Explain or show your reasoning.

Activity #2

`Practice ``Exercise Questions on Comparing Populations Samples. ` • Use the dot plot samples below to answer the questions that follow.

Consider the question: Do tenth-grade students’ backpacks generally weigh more than seventh-grade students’ backpacks? Here are dot plots showing the weights of backpacks for a random sample of students from these two grades:

(2.) The mean weight of this sample of seventh-grade backpacks is 6.3 pounds. Do you think the mean weight of backpacks for all seventh-grade students is exactly 6.3 pounds?

(3.) The mean weight of this sample of tenth-grade backpacks is 14.8 pounds. Do you think there is a meaningful difference between the weight of all seventh-grade and tenth-grade students’ backpacks? Explain or show your reasoning.

Here are 10 more random samples of seventh-grade students’ backpack weights.

(4.) Which sample has the highest mean weight?

(5.) Which sample has the lowest mean weight?

(6.) What is the difference between these two sample means?

(7.) All of the samples have a mean absolute deviation of about 2.8 pounds. Express the difference between the highest and lowest sample means as a multiple of the MAD.

(8.) Are these samples very different? Explain or show your reasoning. Challenge #1

Lin wants to know if students in elementary school generally spend more time playing outdoors than students in middle school. She selects a random sample of size 20 from each population of students and asks them how many hours they played outdoors last week. Suppose that the MAD for each of her samples is about 3 hours.

Challenge #2

A farmer grows 5,000 pumpkins each year. The pumpkins are priced according to their weight, so the farmer would like to estimate the mean weight of the pumpkins he grew this year. He randomly selects 8 pumpkins and weighs them. Here are the weights (in pounds) of these pumpkins: