STEPS SOLUTIONS 1. Arrange the data in ascending order. 2. Locate the position of the given data. 3. Interpolate a. Find the difference ... b. Multiply the result ... c. Add the result ... 4. Interpret the result

Below is an explanation of each step when using linear interpolation to estimate an unknown value between known data points: 1. Arrange the data in ascending order.  • List your known values (for both the independent variable, often x, and the dependent variable, often y) from smallest to largest.  • This ensures you can easily find the two data points between which your unknown value lies. 2. Locate the position of the given data.  • Identify the interval that contains the given value of x (or whatever independent variable you’re using).  • In other words, find the two consecutive data points (x₁, y₁) and (x₂, y₂) such that x₁ ≤ x (given) ≤ x₂. 3. Interpolate.  a. Find the difference between the given value and the lower bound of the interval.   • Compute (x – x₁). This tells you how far your point is from the lower known data point.  b. Multiply the difference by the ratio of the change in y over the change in x.   • Calculate the ratio (y₂ – y₁) / (x₂ – x₁).   • Multiply (x – x₁) by this ratio to see how much the dependent variable should change relative to the given x.  c. Add the result to the lower y-value to obtain the interpolated value.   • That is, y = y₁ + (x – x₁) × [(y₂ – y₁) / (x₂ – x₁)]. 4. Interpret the result.  • The computed value of y is your estimation for the unknown point corresponding to the given x.  • Ensure the result makes sense in the context of your data, and note that this linear interpolation provides an estimate assuming a straight-line change between the known points. By following these steps, you correctly position your new data point between the given range and estimate the corresponding value using the linear relationship between the two adjacent known points.