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# Lesson 6 Homework Practice Compare Populations Answers

Lesson 6 Homework Practice Compare Populations Answers

## Lesson 6 Homework Practice Compare Populations Answers

In this lesson, you will learn how to compare two populations using statistical measures such as mean, median, mode, range, and standard deviation. You will also learn how to use box plots and histograms to display and compare data sets. You will apply these skills to solve real-world problems involving population data.

## What are populations and samples?

A population is a set of all individuals or objects that share one or more characteristics. For example, the population of the United States is the set of all people who live in the country. A sample is a subset of a population that is selected for a study or an experiment. For example, a sample of the population of the United States could be the set of 1000 people who responded to a survey.

When comparing two populations, it is often impractical or impossible to collect data from every individual or object in the populations. Therefore, we use samples to make inferences or generalizations about the populations. However, we need to be careful when choosing samples, because they may not be representative of the populations. For example, if we want to compare the heights of students in two schools, we need to select samples that are random and have similar sizes.

## How to compare two populations using statistical measures?

One way to compare two populations is to use statistical measures that describe the center and spread of the data sets. The center of a data set is a value that represents the typical or average value of the data. The spread of a data set is a measure of how much the data values vary or differ from each other. Some common statistical measures are:

• Mean: The sum of all data values divided by the number of data values.

• Median: The middle value of a data set when it is ordered from least to greatest.

• Mode: The most frequent value or values in a data set.

• Range: The difference between the maximum and minimum values in a data set.

• Standard deviation: A measure of how much the data values deviate from the mean.

To compare two populations using these measures, we can calculate them for each sample and then compare them. For example, if we want to compare the heights of students in two schools, we can find the mean, median, mode, range, and standard deviation of the heights of each sample and then see which school has higher or lower values for each measure. This can help us determine which school has taller or shorter students on average, which school has more or less variation in heights, and which school has more or less outliers in heights.

## How to compare two populations using box plots and histograms?

Another way to compare two populations is to use graphical displays that show the distribution and shape of the data sets. Two common graphical displays are:

• Box plot: A diagram that shows the five-number summary of a data set: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. The box plot also shows any outliers, which are data values that are much higher or lower than the rest of the data.

• Histogram: A graph that shows the frequency of data values in intervals or bins. The height of each bar represents the number of data values in each bin.

To compare two populations using these displays, we can draw them for each sample and then compare them visually. For example, if we want to compare the weights of dogs in two shelters, we can make box plots and histograms of the weights of each sample and then see which shelter has higher or lower values for each summary statistic, which shelter has more or less outliers in weights, and which shelter has more or less symmetric or skewed distributions in weights.

## Examples

Here are some examples of how to compare two populations using statistical measures and graphical displays:

• The table below shows the scores on a math test for two classes: Class A and Class B. Compare the two classes using mean, median, mode, range, and standard deviation.

Class A Class B ------------------ 85 90 92 88 78 95 81 82 87 86 94 91 79 89 83 93 Solution:

To compare the two classes using mean, median, mode, range, and standard deviation, we need to calculate these measures for each class. We can use a calculator or a spreadsheet to do this. The results are shown below:

Measure Class A Class B ---------------------------------- Mean 84.875 89.125 Median 84 89.5 Mode None None Range 16 13 Standard deviation 5.67 3.77 To compare the two classes, we can look at the values of each measure and see which class has higher or lower values. For example, we can see that:

• Class B has a higher mean than Class A, which means that Class B has a higher average score than Class A.

• Class B has a higher median than Class A, which means that the middle score of Class B is higher than the middle score of Class A.

• Neither class has a mode, which means that there is no score that occurs more frequently than any other score in either class.

• Class A has a larger range than Class B, which means that the difference between the highest and lowest scores in Class A is greater than the difference in Class B.

• Class A has a larger standard deviation than Class B, which means that the scores in Class A are more spread out or vary more from the mean than the scores in Class B.

Based on these comparisons, we can conclude that Class B performed better than Class A on the math test, and that Class A had more variation in scores than Class B.

• The histograms below show the ages of customers who visited two stores: Store X and Store Y. Compare the two stores using the histograms.

![Histograms] Solution:

To compare the two stores using the histograms, we need to look at the shape and distribution of the data sets. We can use the following questions to guide our comparison:

• Which store has more customers in each age group?

• Which store has more customers overall?

• Which store has a younger or older customer base?

• Which store has a more symmetric or skewed distribution of ages?

Based on these questions, we can make the following observations:

• Store X has more customers in the age groups of 20-29 and 30-39, while Store Y has more customers in the age groups of 40-49 and 50-59.

• Store X has more customers overall than Store Y, as the total height of its bars is greater than the total height of Store Y's bars.

• Store X has a younger customer base than Store Y, as its bars are higher on the left side of the graph, which represents lower ages.

• Store X has a more symmetric distribution of ages than Store Y, as its bars are roughly balanced around the middle. Store Y has a right-skewed distribution of ages, as its bars are higher on the right side of the graph, which represents higher ages.

Based on these comparisons, we can conclude that Store X attracts more and younger customers than Store Y, and that Store Y has a more uneven distribution of ages than Store X.

• The box plots below show the heights (in inches) of male and female students in a school. Compare the two populations using the box plots.

![Box plots] Solution:

To compare the two populations using the box plots, we need to look at the five-number summary and outliers of each data set. We can use the following questions to guide our comparison:

• Which population has higher or lower values for each summary statistic?

• Which population has more or less variation in heights?

• Which population has more or less outliers in heights?

Based on these questions, we can make the following observations:

• The male population has higher values for each summary statistic than the female population, as its box plot is shifted to the right of the female box plot on the number line.

• The male population has more variation in heights than the female population, as its box plot is longer and has a larger interquartile range (IQR) than the female box plot. The IQR is the distance between Q1 and Q3, which represents the middle 50% of the data.

• The female population has more outliers in heights than the male population, as its box plot has more dots outside the whiskers than the male box plot. The whiskers are the lines that extend from the box to the minimum and maximum values, excluding outliers. Outliers are data values that are more than 1.5 times the IQR away from Q1 or Q3.

Based on these comparisons, we can conclude that the male population is taller than the female population on average, and that the female population has more extreme values in heights than the male population. I have already written an HTML article for the keyword "Lesson 6 Homework Practice Compare Populations Answers" in the previous turn. Do you want me to write another article on a different topic? If so, please provide me with a new keyword. If not, please let me know if you have any questions or feedback about the article I wrote. Thank you for usi

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