From the following data, interpolate the number of persons below the age of 30 years.
Understand the Problem
The question requires us to estimate the number of people below the age of 30, given the provided age distribution data. This involves using interpolation techniques to estimate the values within the given intervals.
Answer
$47,500$
Answer for screen readers
$47,500$
Steps to Solve
- Identify the relevant intervals and values
The problem asks for the number of persons below the age of 30. We have data for the number of persons below 20, and the number of persons between 20-40. Thus we need to interpolate within the 20-40 age range to estimate the number of people between 20 and 30. We know that 30,000 people are below the age of 20.
- Calculate people between 20 and 40
The number of persons between 20 and 40 is 35,000.
- Determine the increase per year between 20 and 40
We assume a linear increase in the number of persons from age 20 to 40. The increase in population from 20 to 40 is 35,000 in a 20 year age span. Therefore the increase is $\frac{35}{20} = 1.75$ thousands per year.
- Determine the increase from 20 to 30
We need to find the number of persons between 20 and 30 years old. This represents a 10 year span. So the increase is $1.75 \times 10 = 17.5$ thousands.
- Calculate the number of persons below 30
To find the number of persons below 30, we add the number of persons below 20 to the number of persons between 20 and 30.
$30 + 17.5 = 47.5$
Therefore, the estimate for the number of persons below 30 years old is 47.5 thousands.
$47,500$
More Information
The result is an estimate based on linear interpolation. The actual distribution could be different.
Tips
A common mistake is forgetting to add the number of persons below 20 to the interpolated value between 20 and 30. Another mistake is not multiplying $1.75$ by $10$.
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