The table shows the mark obtained by students in a test.
| Marks | 1 | 2 | 3 | 4 | 5 |
| Frequency | 2 | k | 1 | 1 | 2 |
If the mean mark is 3, find the value of k.
- 4
-
1
- 2
- 3
The correct answer is: B
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