Q. 435.0( 2 Votes )

Which is false?
A. If the mean of 4, 6, x, 8, 10, 13 is 8, then x = 7.

B. If the median of the following array 59, 62, 65, x , x + 2, 72, 85, 99 is 67, then x = 66.

C. If the mode of 1, 3, 5, 7, 5, 2, 7, 5, 9, 3, p, 11 is 5, then the value of p is 7.

D. If the mean of 10 observations is 15 and that of other 15 observations is 18, then the mean of all the 25 observations is 16.8.

Answer :

(A) Given observations are = 4, 6, x, 8, 10, 13


Mean =


Now, given mean = 8



Sum of the observations = 4 + 6 + x + 8 + 10 + 13 = 8 × 6


41 + x = 48


x = 48 – 41 = 7


So, x = 7


The given statement is true.


(B) Given array = 59, 62, 65, x, x + 2, 72, 85, 99


n = 8 (even)


Median = 1/2 [value of (n/2)th term + value of (n/2 + 1)th term]


= 1/2 [value of 4th term + value of 5th term]


Median =


Given median = 67


67 = 2x + 2 = 67 × 2


2x + 2 = 134


2x = 134 – 2


X = = 66


So, x = 66


The given statement is true


(C) Given,


Observations are = 1, 3, 5, 7, 5, 2, 7, 5, 9, 3, p, 11


Mode = 5


Value of p = 7


We know that mode is the item which has highest frequency and in given statement 5 is the mode. If p = 7 then it will become the number with highest frequency. It means p can’t be equals to 7 as mode is 5.


So, the given statement is false.


(D) Given;


Mean of 10 observations = 15


Mean of 15 observations = 18


Mean of all 25 observation = 16.8


Now the sum of the observations;


Sum of 10 observations = 10 × 15 = 150


Sum of 15 observation = 15 × 18 = 270


Sum of 25 observation = Sum of 10 observations + Sum of 15 observations


Mean of 25 observations =


Mean =


Mean = 420/25


Mean = 16.8


So, the given statement is true.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses