The table shows the mark obtained by students in a test. Marks 1 2 3…

Explanation

 x̄ \(=\frac{∑fx}{∑f}= 3\)

\(=\frac{(1 \times 2)+(2 \times k)+(3 \times 1)+(4 \times 1)+(5 \times 2)}{2 + k + 1 + 1 + 2}= 3\)

\(=\frac{2 + 2k + 3 + 4 + 10}{6 + k} = 3\)

\(=\frac{19 + 2k}{6 + k} = 3\)

\(=\frac{19 + 2k}{6 + k} = \frac{3}{1}\)

=19+2k=3(6+k)

=19+2k=18+3k

=2k-3k=18-19

=-k=-1

∴k=1