Question

Use the assumed-mean method to find the mean height of the plants from the following frequency-distribution table.

Height in cm (xi)	61	64	67	70	73
No. of plants (fi)	5	18	42	27	8

Answer 1

Let the assumed mean be A = 67.
Now, we will make the following table:

Height in cm (xi)	No. of Plants (fi)	di = (xi$-$A)= (xi$-$67)	(fi)(di)
61	5	$-$6	$-$30
64	18	$-$3	$-$54
67	42	0	0
70	27	3	81
73	8	6	48
	$\sum _{}^{}{f}_i=$100		$\sum _{}^{}{f}_{i}di=$45

Thus, we have:
$\mathrm{Mean}=\overline{\mathrm{x}}=A+\frac{{\displaystyle \underset{}{\overset{}{\sum f_i{d}_i}}}}{{\displaystyle \sum _{}^{}}{f}_i}$
$$\begin{gathered} =67+\frac{\left(45\right)}{100} \\ =\frac{6700+45}{100} \\ =\frac{6745}{100} \\ =67.45\mathrm{cm} \end{gathered}$$