Solution:

(i) Mean of 1, 7, 5, 3, 4, 4 is m.

Here n = 6

Mean, m = (1+7+5+3+4+4)/6

m = 24/6

m = 4

Given the numbers 3, 2, 4, 2, 3, 3, p have mean m-1.

So m-1 = (3+2+4+2+3+3+p)/7

4-1 = (17+p)/7

3 = (17+p)/7

3×7 = 17+p

21 = 17+p

p = 21-17

p = 4

Hence the value of p is 4.

(ii) Given the numbers have median q.

Arranging them in ascending order

2, 2, 3, 3, 3, 4, 4

Here n = 7 which is odd

So median = ((n+1)/2)^th term

q = ((7+1)/2 )^th term

q = (8/2 )^th term

q = 4^th term

q = 3

So value of q is 3.

(iii)mean of p and q = (p+q)/2

= (4+3)/2

= 7/2

= 3.5

Hence the mean of p and q is 3.5.