Below are the scores of a group of students in a test \(\begin{array}{c|c} Scores &...

JAMB 1990

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

A. 1
B. 2
C. 3
D. 4

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Correct Answer: Option 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

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