I have a question:-
->Find the mean of the following distribution:
x:15   17   19   20+p   23
f: 2    3     4    5p       6

Asked by Amrut Kurtkoti | 10th Dec, 2014, 08:15: PM

Expert Answer:

Please check the question:
Question should be:
Find the value of p if the mean of the following distribution is 20.
x 15 17 19 20+p 23
f 2 3 4 5p 6
 
Solution:
Let us construct the following table:
x f f cross times x
15 2 30
17 3 51
19 4 76
20+p 5p 100 p plus 5 p squared
23 6 138
 
Given that mean is 20
We know that M e a n equals fraction numerator begin display style sum from i equals 1 to n of end style f subscript i cross times x subscript i over denominator begin display style sum from i equals 1 to n of end style f subscript i end fraction
T h a t space i s comma space 20 equals fraction numerator 30 plus 51 plus 76 plus 100 p plus 5 p squared plus 138 over denominator 2 plus 3 plus 4 plus 5 p plus 6 end fraction rightwards double arrow space 20 equals fraction numerator 100 p plus 5 p squared plus 295 over denominator 15 plus 5 p end fraction rightwards double arrow 20 open parentheses 15 plus 5 p close parentheses equals 100 p plus 5 p squared plus 295 rightwards double arrow 4 open parentheses 15 plus 5 p close parentheses equals 20 p plus p squared plus 59 rightwards double arrow 60 plus 20 p equals 20 p plus p squared plus 59 rightwards double arrow 1 equals p squared rightwards double arrow p equals 1

Answered by Vimala Ramamurthy | 11th Dec, 2014, 08:53: AM