Four samples of size 50, 100, 150 and 200 have mean height respectively as 40.4, 45.2, 48.4 and50.0 cms. Their combined mean height is (cm)

The correct answer is (c) 49.4.

The combined mean height is calculated by taking the sum of the products of each sample mean and its sample size, and dividing by the total sample size. In this case, the total sample size is $50 + 100 + 150 + 200 = 500$. The sum of the products of each sample mean and its sample size is $40.4 \times 50 + 45.2 \times 100 + 48.4 \times 150 + 50.0 \times 200 = 49400$. Therefore, the combined mean height is $\frac{49400}{500} = 49.4$ cm.

Option (a) is incorrect because it is the mean height of the first two samples only. Option (b) is incorrect because it is the mean height of the second two samples only. Option (d) is incorrect because it is the mean height of the third and fourth samples only.