If mean of the data 5, 6, 8, 13, p+3, 8, 3 is 7 and its median is q, then find $\sqrt{p+q}$.

3

mean of the data 5, 6, 8, 13, p+3, 8, 3 is 7.

Mean = (5+6+8+13+p+3+8+3)/7 = (46+p)/7 = 7

46+p = 49

p = 3

the data 5, 6, 8, 13, 6, 8,3 

Number of observations = 7

Rearranging the terms = 3,5,6,6,8,8,13

median = 4th term = q = 6

$\sqrt{p+q} = \sqrt{3+6}$ = 3

The correct answer is Option (1) → 3