What is the difference between the total number of male viewers and female…

Concept

When a total T is divided in the ratio M:F = m:f, the male count is T × m/(m + f), the female count is T × f/(m + f), and the signed male-minus-female difference is T × (m - f)/(m + f).

Add the signed differences across all groups to obtain the overall male-minus-female balance. The requested difference is the absolute value of that balance.

Application

1. City A: 2346 × (2 - 1)/(2 + 1) = 2346/3 = 782.

2. City B: 3094 × (8 - 9)/(8 + 9) = -3094/17 = -182.

3. City C: 2610 × (3 - 2)/(3 + 2) = 2610/5 = 522.

4. City D: 2976 × (7 - 9)/(7 + 9) = -5952/16 = -372.

5. City E: 2670 × (8 - 7)/(8 + 7) = 2670/15 = 178.

6. City F: 2398 × (5 - 6)/(5 + 6) = -2398/11 = -218.

7. Overall signed balance = 782 - 182 + 522 - 372 + 178 - 218 = 710. Therefore, the required difference is |710| = 710 viewers.

Cross-check

The independently summed totals give 8402 - 7692 = 710, confirming the result.