Question

You grew sixty plants using special soil. You measure their lengths and the values are tabulated below.

Length(cm)	$120-125$	$125-130$	$130-135$	$135-140$	$140-145$	$145-150$
Number of plants	$8$	$10$	Y	$16$	$8$	$12$

The mean length of the plants is $136$cm. Find y in the table.

• A. $10$
• B. $8$
• C. $6$
• D. $4$

Answer 1

The correct option is C $6$

Length(cm) $\left(f_i\right)$ $x_i$ $f_i{x}_i$

$120-125$ $8$ $122.5$ $122.5\times 8=980$

$125-130$ $10$ $127.5$ $127.5\times 10=1275$

$130-135$ Y $132.5$ $y\times 132.5=132.5y$

$135-140$ $16$ $137.5$ $137.5\times 16=2200$

$140-145$ $8$ $142.5$ $142.5\times 8=1140$

$145-150$ $12$ $147.5$ $147.5\times 12=1770$

$\Sigma f_i=60$ $\Sigma f_i{x}_i=7365+795y$

Arithmetic mean using direct method formula is $\overline{x}=\frac{\Sigma f_i{x}_i}{\Sigma f_i}$

$136=(7365+795y)/60$

$136\times 60=7365+132.5y$

$8160-7365=132.5y$

$y=\frac{795}{132.5}$

$y=6$

Therefore, the value of y is $6$.