(a) Find the mean of the following data :

18, 33, 30, 21 and 13.

Also, find the sum of deviations of this data from the mean.

(b) If 150 is the mean of 200 observations and 100 is the mean of some 300 other observations, find the mean of the combination.

The mean of a certain number of observations is 35. What is the new value of the mean if each observation is :

(i) increased by 7.

(ii) decreased by 5.

(iii) multiplied by 2.

(iv) divided by 5.

(v) increased by 20%.

(vi) decreased by 30%.

The following data have been arranged in ascending order of magnitude.

63, 66, 69, x, x + 2, 76, 89 and 103.

If the median of the given data is 71, find the value of x.

(a) An isosceles right-angled triangle has area 200 cm². What is the length of its hypotenuse?

(b) The perimeter of a triangle is 540 m and its sides are in the ratio 12 : 25 : 17. Find the area of the triangle.

(c) Find the area of triangle whose sides are 5 cm, 12 cm and 13 cm. Also, find the length of its altitude corresponding to the longest side.