Question

Q.6. Estimate the production of eotton in the year 1935 from the data given below: \begin{tabular}{|l|l|l|l|l|l|l|l|} \hline Year \( (x) \) & 1931 & 1932 & 1933 & 1934 & 1935 & 1936 & 1937 \\ \hline Production & 17.1 & 13 & 14 & 9.6 & - & 12.4 & 18.2 \\ \hline \end{tabular} Ans. Let missing teun \( f(1935)=a \) \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline\( x \) & \( f(x) \) & \( \Delta f(x) \) & \( \Delta^{3} f(x) \) & \( \Delta^{3} f(x) \) & \( \Delta^{4} f(x) \) & \( \Delta^{5} f(x) \) & \( \Delta^{6} f(x) \) \\ \hline 1931 & 17.1 & -4.1 & & & & & \\ \hline 1932 & 13 & 1 & 5.1 & -10.5 & & & \\ \hline 1983 & 14 & -4.4 & -5.4 & \( a+0.2 \) & \( a+10.7 \) & \( -5 a+16.3 \) & \\ \hline 1934 & 9.6 & \( a-9.6 \) & \( a-5.2 \) & \( -3 a+27.2 \) & \( -4 a+2.7 \) & \( 10 a-82.8 \) & \( 159-99.1 \) \\ \hline 1935 & \( a \) & \( -a+12.4 \) & \( -2 \alpha+22 \) & \( 3 a-28.6 \) & \( 6 a-55.8 \) & & \\ \hline \begin{tabular}{l} 1936 \\ 1937 \end{tabular} & \begin{tabular}{l} 12.4 \\ 18.2 \end{tabular} & 5.8 & \( a-6.6 \) & & & & \\ \hline \end{tabular} \( \because \) Six values are known to us. \( \because 3 \) values are known

          Q.6. Estimate the production of eotton in the year 1935 from the data given below:
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline Year \( (x) \) & 1931 & 1932 & 1933 & 1934 & 1935 & 1936 & 1937 \\
\hline Production & 17.1 & 13 & 14 & 9.6 & - & 12.4 & 18.2 \\
\hline
\end{tabular}

Ans. Let missing teun \( f(1935)=a \)
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline\( x \) & \( f(x) \) & \( \Delta f(x) \) & \( \Delta^{3} f(x) \) & \( \Delta^{3} f(x) \) & \( \Delta^{4} f(x) \) & \( \Delta^{5} f(x) \) & \( \Delta^{6} f(x) \) \\
\hline 1931 & 17.1 & -4.1 & & & & & \\
\hline 1932 & 13 & 1 & 5.1 & -10.5 & & & \\
\hline 1983 & 14 & -4.4 & -5.4 & \( a+0.2 \) & \( a+10.7 \) & \( -5 a+16.3 \) & \\
\hline 1934 & 9.6 & \( a-9.6 \) & \( a-5.2 \) & \( -3 a+27.2 \) & \( -4 a+2.7 \) & \( 10 a-82.8 \) & \( 159-99.1 \) \\
\hline 1935 & \( a \) & \( -a+12.4 \) & \( -2 \alpha+22 \) & \( 3 a-28.6 \) & \( 6 a-55.8 \) & & \\
\hline \begin{tabular}{l}
1936 \\
1937
\end{tabular} & \begin{tabular}{l}
12.4 \\
18.2
\end{tabular} & 5.8 & \( a-6.6 \) & & & & \\
\hline
\end{tabular}
\( \because \) Six values are known to us.
\( \because 3 \) values are known

Q.6. Estimate the production of eotton in the year 1935 from the data given below:

Year (x) 1931 1932 1933 1934 1935 1936 1937

Production 17.1 13 14 9.6 - 12.4 18.2

Ans. Let missing teun f(1935)=a

x f(x) Δ f(x) Δ^3 f(x) Δ^3 f(x) Δ^4 f(x) Δ^5 f(x) Δ^6 f(x)

1931 17.1 -4.1

1932 13 1 5.1 -10.5

1983 14 -4.4 -5.4 a+0.2 a+10.7 -5 a+16.3

1934 9.6 a-9.6 a-5.2 -3 a+27.2 -4 a+2.7 10 a-82.8 159-99.1

1935 a -a+12.4 -2 α+22 3 a-28.6 6 a-55.8

1936

1937

12.4

18.2
5.8 a-6.6

∵ Six values are known to us.
∵ 3 values are known

Added by Joseph A.

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