What is the average number of female viewers of Zee TV taking all six cities…

Concept

When a total is split between two groups in the ratio M : F, the second group’s share is F/(M + F) of that total, so its count is Total × F/(M + F). The arithmetic mean of n quantities is their sum divided by n.

Putting the two together: to average one group’s strength across several rows of a table, first convert every row’s total into that group’s count, then add those counts and divide by the number of rows. Averaging the totals first, or averaging the ratios, is not the same thing and gives a different figure.

Application

Only the two ZEE columns are used; the JIO, SONY and COLORS figures play no part in this question. For each city, female ZEE viewers = ZEE total × F/(M + F).

1. Add the six female counts in order: 782 + 1638 = 2420; 2420 + 1044 = 3464; 3464 + 1674 = 5138; 5138 + 1246 = 6384; 6384 + 1308 = 7692.

2. Divide the combined count by the number of cities: 7692 ÷ 6 = 1282.

Cross-check

• Re-add in pairs, in a different order: (782 + 1638) + (1044 + 1674) + (1246 + 1308) = 2420 + 2718 + 2554 = 7692, which matches the running total.

• Multiply back: 1282 × 6 = 7692 reproduces the combined female count, so the mean is consistent with the six city figures.

• Every ZEE total is exactly divisible by the sum of its own ratio parts (2346 by 3, 3094 by 17, 2610 by 5, 2976 by 16, 2670 by 15, 2398 by 11), so no rounding enters at any step and the average is a whole number.

Hence the average number of female ZEE viewers across all six cities is 1282.