Question

the mean of 1,3,4,5,7 is m. the numbers3,2,2,4,3,3,p have mean(m-1)and median q then p+q=

Answer 1

Mean of 1,3,4,5,7 = Sum of all the items/ no. of items

= (1 + 3 + 4 + 5 + 7)/5
= 20/5 = 4
Hence m =4. ----(1)
Similarly,
Mean of 3,2,2,4,3,3,p. = m-1 = 4 - 1 = 3
(3 + 2 + 2 + 4 + 3 + 3 + p)/7 = 3
(17 + p )/7 = 3
Transposing 7 to right.
17 + p = 21
Transposing 16 to right.
p = 4 ---(2)

Calculation of median :- 3,2,2,4,3,3,4
Ascending order = 2,2,3,3,3,4,4
No. of items = 7 i.e. odd
Hence Median = (n + 1)/2 this term
= (7+1)/2 th term
= 8/2 th term
= 4th term
4 th term of Ascending order is 3.
Hence median = 3 i.e. q = 3----(3)

now p + q = 4 + 3 = 7

Answer 2

mean = sum of observations/total number of observations
m = (1 + 3 + 4 + 5 + 7)/5 = (4 + 4 + 12)/5
m = 20/5 = 4 .........(i)

again, the numbers 3, 2, 2, 4, 3,3 , p have mean (m - 1)
so, (m - 1) = (3 + 2 + 2 + 4 + 3 + 3 + p)/7
from equation (i),
(4 - 1) = (17 + p)/7
21 = 17 + p
p = 21- 17 = 4

now, numbers 3, 2,2,4,3,3,p have median q
first of all, arrange in ascending,
2 , 2, 3 , 3, 3, 4 , p total number of observations= 7 { odd number}
so, medain = (n + 1)/2 th term
q = (7 + 1)/2 = 4th term = 3

hence, p + q = 4 + 3 = 7