Lesson 6 Homework Tips: Comparing Populations with Measures of Center and Spread

Lesson 6 Homework Practice Compare Populations Answers

If you are taking a course in statistics and probability, you might be wondering how to do your homework for Lesson 6. In this lesson, you will learn how to compare two populations using sample statistics, such as mean, median, interquartile range, and mean absolute deviation. You will also learn how to make informal inferences about the difference between two populations based on samples of the same size from each population. In this article, we will explain what Lesson 6 is about, give you some examples of exercises, and show you how to check your answers.

Lesson 6 Homework Practice Compare Populations Answers

What is Lesson 6 about?

Lesson 6 is about comparing populations using sample statistics. A population is a set of all individuals or objects that have one or more characteristics in common. For example, the population of all students in your school, or the population of all cars in your city. A sample is a subset of a population that is selected randomly or systematically. For example, a sample of 50 students from your school, or a sample of 20 cars from your city.

Sample statistics are numerical measures that describe some aspect of a sample, such as its center or its spread. The center of a sample is a value that represents the typical or average data value in the sample. The most common measures of center are mean and median. The mean is the sum of all the data values in a sample divided by the number of data values. The median is the value that separates the upper half of the distribution of a sample from the lower half. The spread of a sample is a measure of how much the data values vary or differ from each other. The most common measures of spread are interquartile range and mean absolute deviation. The interquartile range is the difference between the upper quartile and the lower quartile of a sample. The upper quartile is the median of the upper half of the sample, and the lower quartile is the median of the lower half of the sample. The mean absolute deviation is the mean of the absolute values of all deviations from the mean of a sample.

Comparing populations using sample statistics means using measures of both center and spread to make informal inferences about the difference between two populations based on samples from those populations. Informal inferences are logical conclusions that are not based on formal rules or procedures, but on reasoning and evidence. For example, if you have two samples of students' test scores from two different classes, you can compare their means and their interquartile ranges to make an informal inference about which class performed better on average and which class had more variation in their scores.

What are some examples of Lesson 6 exercises?

Here are some examples of exercises that you might encounter in Lesson 6 homework. For each exercise, you will be given two samples from two different populations, and you will have to compare their centers and variations, and write an inference you can draw about the two populations.

Example 1: Fitness club daily attendance

The double plot shows the daily attendance for two fitness clubs for one month.

To compare the centers and variations of the two samples, you can use these steps:

• Find the mean and median for each sample by adding up all the data values and dividing by the number of data values (for mean), and by finding the middle value or the average of the middle two values (for median).

• Find the interquartile range for each sample by finding the upper quartile (the median of the upper half) and subtracting it from the lower quartile (the median of the lower half).

• Compare the means, medians, and interquartile ranges of the two samples and see which one has a higher or lower value.

Using these steps, you can find that:

• The mean for Fun Fit is 100 with a variation of 30.

• The mean for Greg's Gym is 120 with a variation of 20.

• The median for Fun Fit is also 100 with an interquartile range of 20.

• The median for Greg's Gym is also 120 with an interquartile range of 10.

An inference you can draw about the two populations based on these sample statistics is:

Overall, Greg's Gym has a greater attendance with less variation than Fun Fit.

Example 2: Weights of housecats and small dogs

The double dot plot shows the weights in pounds of several housecats and small dogs.

To compare the centers and variations of the two samples, you can use these steps:

• Find the mean and median for each sample by adding up all the data values and dividing by the number of data values (for mean), and by finding the middle value or the average of the middle two values (for median).

• Find the mean absolute deviation for each sample by finding the difference between each data value and the mean, taking their absolute values, and finding their average.

• Compare the means, medians, and mean absolute deviations of the two samples and see which one has a higher or lower value.

Using these steps, you can find that:

• The mean for the housecat data is 11 with a variation of about 0.9.

• The mean for the small dog data is 9 with a variation of 1.3.

• The median for the housecat data is also 11 with a mean absolute deviation of 0.8.

• The median for the small dog data is also 9 with a mean absolute deviation of 1.1.

An inference you can draw about the two populations based on these sample statistics is:

Overall, the housecats weigh more with less variation than the small dogs.

Example 3: Gas mileage of cars and SUVs

The double dot plot shows the gas mileage, in miles per gallon, for several cars and SUVs.

To compare the centers and variations of the two samples, you can use these steps:

Find the mean and median for each sample by adding up all the data values and dividing by the number of data values (for mean), and by finding the middle value or the average of the middle two values (for median).