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
Step 1: State the formula for the mean age. The mean age x (in years) is given by x = ( (x_i · f_i))/( f_i) where x_i is the age in years and f_i is the number of girls of that age. Step 2: List the data from the table. c|c Age (years) & Number of girls \\ 11 & 3 \\ 12 & 4 \\ 13 & 2 \\ 14 & 5 \\ 15 & 1 \\ Step 3: Calculate the total number of girls, f_i. f_i = 3 + 4 + 2 + 5 + 1 = 7 + 2 = 9 9 + 5 = 14 14 + 1 = 15 Total number of girls = 15. Step 4: Calculate the total age sum, (x_i · f_i) (in years). 11 × 3 = 33 12 × 4 = 48 13 × 2 = 26 14 × 5 = 70 15 × 1 = 15 (x_i · f_i) = 33 + 48 + 26 + 70 + 15 33 + 48 = 81 81 + 26 = 107 107 + 70 = 177 177 + 15 = 192 Total age sum = 192 years. Step 5: Calculate the mean age. x = (192)/(15) 15 × 12 = 180 192 - 180 = 12 (12)/(15) = 0.8 x = 12 + 0.8 = 12.8 years. The mean age of the girls is 12.8 years. 12.8