This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the calculations for the given data: First, let's organize the given data and calculate necessary values: | Age Group | Frequency (f) | Class Midpoint (x) | Cumulative Frequency (cf) | Deviation (d = x - 37) | fd | | :-------- | :-------------- | :------------------- | :-------------------------- | :----------------------- | :--- | | 10-19 | 6 | 14.5 | 6 | -22.5 | -135 | | 20-29 | 12 | 24.5 | 18 | -12.5 | -150 | | 30-39 | 15 | 34.5 | 33 | -2.5 | -37.5 | | 40-49 | 9 | 44.5 | 42 | 7.5 | 67.5 | | 50-59 | 5 | 54.5 | 47 | 17.5 | 87.5 | | 60-69 | 2 | 64.5 | 49 | 27.5 | 55 | | Total | f = 49 | | | | fd = -112.5 | 1) Calculate the mean using an assumed mean of 37. Step 1: Identify the assumed mean (A), sum of frequencies ( f), and sum of fd ( fd). Given assumed mean A = 37. From the table, f = 49 and fd = -112.5. Step 2: Apply the formula for the mean using an assumed mean.