Solve the Problem Draw a Scatter Diagram of the Data for One Period

question 118

Essay

Solve the problem.
-The following data represents the average percent of possible sunshine for a certain city in Indiana. $\begin{array}{l|c}\text { Month, x } & \begin{array}{c}\text { Average Percent of } \\\text { Possible Sunshine }\end{array} \\\hline \text { January, 1 } & 46 \\\text { February, 2 } & 51 \\\text { March, 3 } & 55 \\\text { April, 4 } & 60 \\\text { May, 5 } & 68 \\\text { June, 6 } & 73 \\\text { July, 7 } & 75 \\\text { August, 8 } & 74 \\\text { September, 9 } & 68 \\\text { October, 10 } & 62 \\\text { November, 11 } & 41 \\\text { December, 12 } & 38\end{array}$
Draw a scatter diagram of the data for one period. Find the sinusoidal function of the form $y = A \sin ( \omega x - \varphi ) + B$ fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.

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Definitions:

Herfindahl-Hirschman Index

A measure of market concentration used to determine the level of competition within an industry.

Market Share

The portion of a market controlled by a particular company or product.

Oligopolistic Models

Economic models that describe markets in which a few firms dominate, often leading to pricing and output decisions that consider the actions of competitors.

Cartel

An agreement among competing firms to control prices or exclude entry of a new competitor in a market, often in order to maximize the members' profits at the expense of consumers.