Show steps for all problems. Attach the original Excel files, including the answer report and the sensitivity report for the LP models, and time series forecasting files.

Progress Check Use this activity to assess whether you and your peers can:  Describe the shape for a distribution of a quantitative variable. Describe the center for a distribution of a quantitative variable. Describe the spread for a distribution of a quantitative variable. Use dotplots to compare shape, center, and spread in the distribution of a quantitative variable for two groups of individuals. Learn by Doing Use the rubric at the bottom of this page as a guide for completing this assignment. Directions Submit your work: Carefully read all sections below (beginning with the Context section and ending with the Prompt section). Commit a good-faith effort to address all items in the Prompt section below. Please be sure to number your responses. Complete your assigned peer reviews: After you submit your initial good-faith attempt, continue to the ANSWER(S) page and review your instructor's response. But please do not submit your corrected work yet. Within three days after the due date, return to this assignment and complete your assigned peer reviews (directions (Links to an external site.)). Submit your corrected work: We all learn from mistakes (our own and our classmates' mistakes). So please do not immediately correct your own mistakes. If possible, wait until you receive feedback from at least one of your peers.  If necessary, correct your work and resubmit the entire assignment. Your instructor will only review and grade your most recent submission. Module 4 - Dotplots (7 of 22) Describing Center and Spread To describe the pattern in a distribution of a quantitative variable, we describe more than the shape. We also describe the center and spread. Later in this module, we develop more precise ways to identify the center of a distribution and to measure the spread. For now, we discuss these concepts informally. Introduction to the Concept of Center When we describe a distribution of a quantitative variable, it is helpful to identify a typical value. We choose a single value of the variable to represent the entire group. This is one way to think about the center of the distribution. Introduction to the Concept of Spread We also want to describe how much the data varies among individuals in the group. Variability is another word for spread. We describe the spread in two ways: We look at the smallest value and the largest value to describe an overall range in the data.  We also describe an interval of typical values to represent common variable values for the group. EXAMPLE  Describing shape, center and spread This short movie illustrates how to describe the shape, center and spread of a distribution using a dotplot. (3:52 minutes) EXAMPLE  Comparing the distribution of sugar in adult and child cereals Here we use shape, center, and spread to compare the distribution of sugar content in adult cereals and children’s cereals. Compare the shapes: The sugar content in adult cereals is skewed to the right. Many adult cereals have less than 8 grams of sugar in a serving. A smaller number of adult cereals contain high amounts of sugar. The sugar content for children’s cereals is skewed to the left. Many children’s cereals have more than 8 grams of sugar in a serving, with a smaller number of children’s cereals with low amounts of sugar. Comment:  There is nothing special about the number 8. We chose the number 8 as a convenient reference point to describe the opposite trends in these two distributions. Compare the centers: A typical adult cereal has 3 grams of sugar in a serving. A typical children’s cereal has 12 grams of sugar in a serving. Comment: Here we looked at the most common value in each distribution. We develop more precise ways to describe the center of a distribution in the next section. For now, just choose a reasonable typical value to represent the group. Compare the spreads: Overall interval and range: Adult cereals vary from 0 to 14 grams of sugar in a serving. Children’s cereals vary from 1 to 15 grams. So both types of cereal vary over a range of 14 grams. (Note: Overall range = highest value – lowest value. For adult cereals: 14 – 0 = 14. For children’s cereals: 15 – 1 = 14) Typical interval: Typical adult cereals have between 0 and 6 grams of sugar in a serving, compared to 9 to 13 grams in typical children’s cereals. Comment: Here we looked at clumps in the data to identify an interval of typical values. We develop more precise ways to describe the spread a distribution in the last two sections of this module. Pulling it altogether: When comparing two distributions, we usually tie all of these ideas into one paragraph. Here is a paragraph that does a good job comparing the two sugar distributions without using formal vocabulary: In this sample, children’s cereals have more sugar per serving than adult cereals. A typical child cereal has 12 grams of sugar in a serving compared to a typical adult cereal with only 3 grams of sugar. Of course sugar amounts vary in both groups. Child cereals vary from 1 to 15 grams of sugar in a serving, compared to 0 to 14 grams for adult cereals. However, even in light of this variability, we can still say that children's cereals have more sugar when we look at how the data falls within these intervals. For example, many adult cereals have 0 to 6 grams of sugar in a serving, but not many child cereals have these small amounts of sugar. Typical children’s cereals to have 9 to 13 grams of sugar per serving, well above the typical amounts found in adult cereals. Here is a paragraph that uses more formal vocabulary to summarize the comparison: In this sample, children’s cereals have more sugar per serving than adult cereals. The distribution of sugar in children’s cereals is skewed left, which means that fewer child cereals have smaller amounts of sugar. Typical children’s cereals have 9 to 13 grams of sugar per serving with a center of about 12 grams. The distribution of sugar in adult cereals is skewed right, which means that fewer adult cereals have larger amounts of sugar. Typical adult cereals have 0 to 6 grams of sugar per serving with a center of about 3 grams. Both groups of cereals have an overall range of 14 grams, with the sugar in a serving of child cereal varying from 1 to 15 grams, compared to adult cereals that vary from 0 to 14 grams. Despite the identical range in sugar amounts for each group, child cereals clearly tend to have larger amounts of sugar when we examine the shape, center and spread in these distributions.