\(\begin{array}{c|c} x & 1 & 2 & 3 & 4 & 5 \\ \hline f & y + 2 & y - 1 & 2y - 3 & y + 4 & 3y - 4\end{array}\)
This table shows the frequency distribution of a data if the mean is \(\frac{43}{14}\), find y
A
1
B
2
C
3
D
4
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
x
1
2
3
4
5
Total
f
y + 2
y - 1
2y - 3
y + 4
3y - 4
8y - 2
fx
y + 2
2y - 2
6y - 9
4y + 16
15y - 20
28y - 13
Mean = \(\frac{\sum fx}{\sum f}\)
\(\therefore \frac{28y - 13}{8y - 2} = \frac{43}{14}\)
\(\implies 14(28y - 13) = 43(8y - 2)\)
\(392y - 182 = 344y - 86\)
\(392y - 344y = -86 + 182 \implies 48y = 96\)
\(y = 2\)
Source: Myschool Past Questions Archive (Record #31113)