Question

Compute the arithmetic mean from the following frequency table:

Hight (in cms.)	58	60	62	64	66	68
Number of Plants	12	14	20	13	8	5

Answer 1

Height (X)	Plants (f)	fX
58 60 62 64 66 68	12 14 20 13 8 5	696 840 1240 832 528 340
	N=Σf= 72	ΣfX=4476

Calculating the arithmetic mean of the above series by direct method:

$$\begin{gathered} \overline{X}=\frac{\Sigma fX}{\Sigma f} \\ \mathrm{or},\overline{X}=\frac{4476}{72} \\ \Rightarrow \overline{X}=62.16\mathrm{cms} \end{gathered}$$

Hence, the mean height of the plant is 62.16 cms