The mean of 1, 3, 4, 5, 7, 4 is m. The numbers 3, 2, 2, 4, 3, 3, p have mean m − 1 and median q. Then, p + q =
(a)4
(b)5
(c)6
(d)7
Answers
SOLUTION :
The correct option is (d) : 7
Ist case :
Given : Mean = m
Numbers are : 1, 3, 4, 5, 7, 4
MEAN = Sum all the values of all the observations/ Total number of observations
m = (1 + 3 + 4 + 5 + 7 + 4)/6
m = 24/6
m = 4
IInd case :
Given : Mean = m - 1 and median q
Numbers are : 3, 2, 2, 4, 3,3, p
MEAN = Sum all the values of all the observations/ Total number of observations
m - 1 = (3 + 2 + 2 + 4 + 3 + 3 + p )/7
m - 1 = (17 + p)/7
7(m - 1) = 17 + p
7m - 7 = 17 + p
7 × 4 - 7 = 17 + p [m = 4]
28 - 7 = 17 + p
21 = 17 + p
p = 21 - 17
p = 4
Arranging the numbers in ascending order are : 2, 2, 3 ,3 ,3 ,4 ,4
n = 7 (odd)
If n is odd then median= value of [(n+1)/2]th observation
Median = (n+1)/2]th term
q = [ (7 + 1) /2 ]th term
q = (8/2)th term
q = 4th term
q = 3
Now, p + q = (4 + 3) = 7
Hence, the value of p + q is 7 .
HOPE THIS ANSWER WILL HELP YOU……
(a)4
(b)5
(c)6
(d)7
Answee: Option D
Explanation:
Given that,
Numbers : 1, 3, 4, 5, 7, 4
MEAN = Sum all the values of all the observations/ Total number of observations
m = (1 + 3 + 4 + 5 + 7 + 4)/6
m = 24/6
m = 4
Now,
Given : Mean = m - 1 and median q
Numbers are : 3, 2, 2, 4, 3,3, p
MEAN = Sum all the values of all the observations/ Total number of observations
m - 1 = (3 + 2 + 2 + 4 + 3 + 3 + p )/7
m - 1 = (17 + p)/7
7(m - 1) = 17 + p
7m - 7 = 17 + p
7 × 4 - 7 = 17 + p [m = 4]
28 - 7 = 17 + p
21 = 17 + p
p = 21 - 17
p = 4
Arranging the numbers in ascending order are : 2, 2, 3 ,3 ,3 ,4 ,4
n = 7 (odd)
If n is odd then median= value of [(n+1)/2]th observation
Median = (n+1)/2]th term
q = [ (7 + 1) /2 ]th term
q = (8/2)th term
q = 4th term
q = 3
Now, p + q = (4 + 3) = 7
Therefore, the value of p + q is 7 .