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 computations for the given data: The table shows the number of children (x_i) and the number of women (f_i): | Number of children (x_i) | Number of women (f_i) | x_i · f_i | Cumulative Frequency | | :------------------------- | :---------------------- | :-------------- | :------------------- | | 0 | 1 | 0 | 1 | | 1 | 5 | 5 | 6 | | 2 | 8 | 16 | 14 | | 3 | 4 | 12 | 18 | | 4 | 2 | 8 | 20 | | Total | f_i = 20 | (x_i f_i) = 41 | | The total number of women (N) is f_i = 20. A) Compute the mean number of children ever born? Step 1: Calculate the sum of (x_i · f_i). (x_i f_i) = (0 × 1) + (1 × 5) + (2 × 8) + (3 × 4) + (4 × 2) = 0 + 5 + 16 + 12 + 8 = 41 Step 2: Calculate the total number of women ( f_i). f_i = 1 + 5 + 8 + 4 + 2 = 20 Step 3: Compute the mean. Mean = ( (x_i f_i))/( f_i) = (41)/(20) = 2.05 The mean number of children ever born is 2.05 children. B) What is the modal number of children ever born? Step 1: Identify the frequency for each number of children. The number of women (frequency) for 0 children is 1. The number of women (frequency) for 1 child is 5. The number of women (frequency) for 2 children is 8. The number of women (frequency) for 3 children is 4. The number of women (frequency) for 4 children is 2. Step 2: Determine the value with the highest frequency. The highest frequency is 8, which corresponds to 2 children. The modal number of children ever born is 2 children. C) What is the median number of children ever born? Step 1: Determine the position of the median. Since the total number of data points (N=20) is even, the median is the average of the (N)/(2)-th and $(N