Question

The following table gives the number of pages written by Sarika for completing her own book for $30$ days

Number of pages written per day $16-18,19-21,22-24,25-27,28-30$

Number of days $1,3,4,9,13$

Find the mean number of pages written per day.

Answer 1

Direct Method of Finding Mean:

Class Marks	Mid – Value$\left({\mathrm{x}}_{\mathrm{i}}\right)$	Number of days $\left({\mathrm{f}}_{\mathrm{i}}\right)$	${\mathrm{f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}$
$15.5–18.5$	$17$	$1$	$17$
$18.5–21.5$	$20$	$3$	$60$
$21.5–24.5$	$23$	$4$	$92$
$24.5–27.5$	$26$	$9$	$234$
$27.5–30.5$	$29$	$13$	$377$
		${\mathrm{\Sigma f}}_{\mathrm{i}}=30$	${\mathrm{\Sigma f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}=780$

The given data is not continuous.

Hence, we subtract $0.5$ from the lower limit and add $0.5$ in the upper limit of each class.

Mean$=\frac{\sum f_i{x}_i}{\sum f_i}$

$$\begin{gathered} =\frac{780}{30} \\ =26 \end{gathered}$$

Therefore, the mean of pages written per day$=26.$