Below are the scores of a group of students..

Question 1 Report

Below are the scores of a group of students in a test:

$\begin{array}{cc} S c o r e s & 1 & 2 & 3 & 4 & 5 & 6 \\ No. of students & 1 & 4 & 5 & 6 & x & 2 \end{array}$

If the average scores is 3.5, find the value of x.

Answer Details

$\begin{array}{cc} S c o r e s & 1 & 2 & 3 & 4 & 5 & 6 \\ No. of students & 1 & 4 & 5 & 6 & x & 2 \end{array}$
Average = 3.5
3.5 = $\frac{(1 \times 1) + (2 \times 4) + (3 \times 5) + (4 \times 6) + 5 x + (6 \times 2)}{1 + 4 + 5 + 6 + x + 2}$
$\frac{3.5}{1}$ = $\frac{1 + 8 + 15 + 24 + 5 x + 12}{18 + x}$
$\frac{3.5}{1}$ = $\frac{60 + 5 x}{18 + x}$
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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