To estimate the population for the year 1925, we will use linear interpolation, as it is a standard method for estimating values between two known data points.

Given data:

We are tasked to estimate the population in 1925, which lies between 1921 and 1931.

Formula for Linear Interpolation:

$P = P_1 + \frac{(P_2 - P_1)}{(t_2 - t_1)} \cdot (t - t_1)$ Where:

• $P_1$ = Population at $t_1$ (starting year),
• $P_2$ = Population at $t_2$ (ending year),
• $t_1$, $t_2$ = Years of $P_1$ and $P_2$,
• $t$ = Year to estimate the population for.

Substituting values:

• $P_1 = 93$ (population in 1921),
• $P_2 = 101$ (population in 1931),
• $t_1 = 1921$,
• $t_2 = 1931$,
• $t = 1925$.

$P = 93 + \frac{(101 - 93)}{(1931 - 1921)} \cdot (1925 - 1921)$

Simplify step-by-step:

1. Difference in population: $101 - 93 = 8$,
2. Difference in years: $1931 - 1921 = 10$,
3. Time interval: $1925 - 1921 = 4$,
4. Population growth per year: $\frac{8}{10} = 0.8$,
5. Population increase from 1921 to 1925: $0.8 \cdot 4 = 3.2$.

$P = 93 + 3.2 = 96.2$

Final Answer:

The estimated population for the year 1925 is 96.2 thousand.

Would you like further details or an explanation?

Here are some related questions you can explore:

1. What is linear interpolation, and how does it work?
2. How do we estimate values beyond the given data range (extrapolation)?
3. What are alternative methods to interpolation for population estimation?
4. How can this data be visualized for better analysis?
5. What is the rate of population growth between 1921 and 1931?

Tip: When using interpolation, always verify if the change is approximately linear, as this assumption underpins the accuracy of the method.