Question

If the mean of the following distribution is 2.6, then the value of y is
variable(x): 1 2 3 4 5
Frequency: 4 5 y 1 2
A. 3
B. 8
C. 13
D. 24

Answer 1

The value of y in the given distribution is 8

Step-by-step explanation:

Given that the mean for the given distribution is 2.6

That is Mean=2.6

Now we have the following table to find $\sum f$ and $\sum fx$ :

Variable       f               fx

_______________________

1                       4                   4

2                      5                  10

3                      y                   3y

4                      1                     4

5                      2                    10

______________________________________

        $\sum f=12+y$           $\sum fx=28+3y$

_______________________________________

Now $Mean=\overline{X}=\frac{\sum fx}{\sum f}$

• $2.6=\frac{28+3y}{12+y}$
• $2.6(12+y=28+3y$
• $2.6(12)+2.6(y)=28+3y$
• $31.2+2.6y=28+3y$
• $31.2-28=3y-2.6y$
• $3.2=0.4y$
• $\frac{3.2}{0.4}=y$
• $8=y$
• Rewritting we get y=8

Therefore the value of y in the given distribution is 8