Question

Use the step-deviation method to find the arithmetic mean from the following data.

x	18	19	20	21	22	23	24
f	170	320	530	700	230	140	110

Answer 1

Here,
h = 1
Let the assumed mean be A = 21.
Now, we will prepare the following table:

(xi)	(fi)	ui = $\frac{\left(x_i-21\right)}{1}$	(ui)(fi)
18	170	$-$3	$-$510
19	320	$-$2	$-$640
20	530	$-$1	$-$530
21 = A	700	0	0
22	230	1	230
23	140	2	280
24	110	3	330
	$\sum _{}^{}{f}_i=$2200		$\sum _{}^{}{f}_i{u}_i=$$-$840

Thus, we have:
$\mathrm{Mean}=\overline{\mathrm{x}}=A+\left(h\times \frac{{\displaystyle \underset{}{\overset{}{\sum f_i{u}_i}}}}{{\displaystyle \sum _{}^{}}{f}_i}\right)$
$$\begin{gathered} =21+\left[1\times \frac{\left(-840\right)}{2200}\right] \\ =21-\frac{840}{2200} \\ =\frac{46200-840}{2200} \\ =\frac{45360}{2200} \\ =20.62 \end{gathered}$$