(begin{array}{c|c} x & 1 & 2 & 3 & 4 & 5 \ hline f & y + 2 & y – 2 & 2y – 3 & y + 4 & 3y – 4end{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
Correct Answer: Option B
Explanation
| 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)