Below are the scores of a group of students in a test
\(\begin{array}{c|c} Scores & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text{No. of students} & 1 & 4 & 5 & 6 & x & 2\end{array}\)
If the average scores is 3.5, find the value of x
- 1
-
2
- 3
- 4
The correct answer is: B
Explanation
\(\begin{array}{c|c} Scores & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text{No. of students} & 1 & 4 & 5 & 6 & x & 2\end{array}\)Average = 3.5
3.5 = \(\frac{(1 \times 1) + (2 \times 4) + (3 \times 5) + (4 \times 6) + 5x + (6 \times 2)}{1 + 4 + 5 + 6 + x + 2}\)
\(\frac{3.5}{1}\) = \(\frac{1 + 8 + 15 + 24 + 5x + 12}{18 + x}\)
\(\frac{3.5}{1}\) = \(\frac{60 + 5x}{18 + x}\)
60 + 5x = 3.5(18 \(\div\) x)
60 + 5x = = 63 + 1.5x
5x - 1.5x = 63 - 60
1.5x = 3
x = \(\frac{3}{1.5}\)
\(\frac{30}{15}\) = 2