Extract the given data for each firm.

Here's the solution to the problem: a) To determine which firm has greater variability in individual wages, we compare their coefficients of variation (CV). The coefficient of variation measures relative variability and is calculated as CV = ()/(x) × 100\%, where is the standard deviation and x is the average wage. Step 1: Extract the given data for each firm. For Firm A: Number of employees (n_A) = 100 Average wage (x_A) = Rs 3200 Variance (_A^2) = 625 For Firm B: Number of employees (n_B) = 150 Average wage (x_B) = Rs 2800 Variance (_B^2) = 729 Step 2: Calculate the standard deviation () for each firm. Standard deviation is the square root of the variance. For Firm A: _A = sqrt(_A^2) = sqrt(625) = 25 For Firm B: _B = sqrt(_B^2) = sqrt(729) = 27 Step 3: Calculate the coefficient of variation (CV) for each firm. For Firm A: CV_A = (_A)/(x)_A × 100\% = (25)/(3200) × 100\% = 0.0078125 × 100\% = 0.78125\% For Firm B: CV_B = (_B)/(x)_B × 100\% = (27)/(2800) × 100\% = 0.009642857 × 100\% ≈ 0.9643\% Step 4: Compare the coefficients of variation. Since CV_B ≈ 0.9643\% is greater than CV_A ≈ 0.78125\%, Firm B has greater variability in individual wages. b) To calculate the average monthly wage and the variance of wages of all workers from both firms combined. Step 1: Calculate the combined average monthly wage (x_combined). The formula for the combined mean is: x_combined = n_A x_A + n_B x_Bn_A + n_B Substitute the values: x_combined = ((100 × 3200) + (150 × 2800))/(100 + 150) x_combined = (320000 + 420000)/(250) x_combined = (740000)/(250) x_combined = 2960 The combined average monthly wage is Rs 2960. Step 2: Calculate the combined variance (_combined^2). The formula for combined variance is: _combined^2 = (n_A(_A^2 + d_A^2) + n_B(_B^2 + d_B^2))/(n_A + n_B) where d_A = x_A - x_combined and d_B = x_B - x_combined. First, calculate the differences (d_A and d_B): d_A = 3200 - 2960 = 240 d_B = 2800 - 2960 = -160 Next, calculate the squared differences (d_A^2 and d_B^2): d_A^2 = (240)^2 = 57600 d_B^2 = (-160)^2 = 25600 Now, substitute these values into the combined variance formula: _combined^2 = (100(625 + 57600) + 150(729 + 25600))/(100 + 150) _combined^2 = (100(58225) + 150(26329))/(250) _combined^2 = (5822500 + 3949350)/(250) _combined^2 = (9771850)/(250) _combined^2 = 39087.4 The combined variance of wages is 39087.4. a) Firm with greater variability: Firm B b) Combined average monthly wage: Rs 2960 Combined variance of wages: 39087.4 Last free one today — make it count tomorrow, or type /upgrade for unlimited.