Bird count The table shows the number of house finches, in...

Bird count The table shows the number of house finches, in thousands, observed in the Christmas bird count in California. $$\begin{array}{|c|c|c|c|c|c|c|}\hline \text { Year } & {1980} & {1985} & {1990} & {1995} & {2000} & {2005} & {2010} \\ \hline \text { Count } & {74} & {92} & {88} & {107} & {70} & {61} & {78} \\ \hline\end{array}$$ (a) Use the data to sketch a rough graph of the bird count as a function of time. (b) Use your graph to estimate the count in 1997.

Bird count The table shows the number of house finches, in thousands, observed in the Christmas bird count in California.
$$\begin{array}{|c|c|c|c|c|c|c|}\hline \text { Year } & {1980} & {1985} & {1990} & {1995} & {2000} & {2005} & {2010} \\ \hline \text { Count } & {74} & {92} & {88} & {107} & {70} & {61} & {78} \\ \hline\end{array}$$

(a) Use the data to sketch a rough graph of the bird count as a function of time.
(b) Use your graph to estimate the count in 1997.

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Key Concepts

Graphical Representation of Data

This concept involves plotting pairs of data points on a coordinate system where one axis represents the independent variable (in this case, time) and the other represents the dependent variable (bird count). The graph helps in visualizing the overall trend and variation in the data over a period.

Interpolation

Interpolation is the process of estimating the value of a function for an intermediate value of the independent variable when only discrete data points are known. In this context, it involves using the graph between the years with known bird counts to estimate the count in a year that was not directly measured.

Time Series Analysis

Time series analysis refers to the method of analyzing a series of data points indexed in time order. It allows one to observe trends, fluctuations, and potential patterns in the data, which is particularly useful when examining how bird counts change over several years.

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