|
Marks
|
$2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ | $11$ | $12$ | $13$ | $14$ | $15$ | $16$ |
|
Frequency
|
$1$ | $6$ | $6$ | $8$ | $8$ | $2$ | $2$ | $3$ | $0$ | $2$ | $1$ | $0$ | $0$ | $0$ | $1$ |
|
$\text{Marks}$
|
$f_i$
|
$f_ix_i$
|
$\text{d}_\text{i}=\text{x}_\text{i}-\bar{\text{x}}$
|
$f_id_i$
|
$f_id_i^2$
|
| $2$ | $1$ | $2$ | $-4$ | $-4$ | $16$ |
| $3$ | $6$ | $18$ | $-3$ | $-18$ | $54$ |
| $4$ | $6$ | $24$ | $-2$ | $-12$ | $24$ |
| $5$ | $8$ | $40$ | $-1$ | $-8$ | $8$ |
| $6$ | $8$ | $40$ | $-1$ | $-8$ | $8$ |
| $7$ | $2$ | $14$ | $1$ | $2$ | $2$ |
| $8$ | $2$ | $16$ | $2$ | $4$ | $8$ |
| $9$ | $3$ | $27$ | $3$ | $9$ | $27$ |
| $10$ | $0$ | $0$ | $4$ | $0$ | $0$ |
| $11$ | $2$ | $22$ | $5$ | $10$ | $50$ |
| $12$ | $1$ | $12$ | $6$ | $6$ | $36$ |
| $13$ | $0$ | $0$ | $7$ | $0$ | $0$ |
| $14$ | $0$ | $0$ | $8$ | $0$ | $0$ |
| $15$ | $0$ | $0$ | $9$ | $0$ | $0$ |
| $16$ | $1$ | $16$ | $10$ | $10$ | $100$ |
|
$Total$
|
$\sum\text{f}_\text{i}=40$
|
$\sum\text{f}_\text{i}\text{x}_\text{i}=239$
|
|
$\sum\text{f}_\text{i}\text{d}_\text{i}=-1$
|
$\sum\text{f}_\text{i}\text{x}^2_\text{i}=325$
|
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