Question

Calculate Mean, Standard Deviation and Variance:

Variable	:	0-5	5-10	10-15	15-20	20-25	25-30	30-35	35-40
Frequency	:	2	5	7	13	21	16	8	3

Answer 1

Variable	Mid Value (m)	Frequency (f)	fm	Deviation Mean $$\begin{gathered} x=\left(m-\overline{\mathrm{X}}\right) \\ \overline{X}=21.9 \end{gathered}$$	x2	fx2
0 − 5 5 − 10 10 − 15 15 − 20 20 − 25 25 − 30 30 − 35 35 − 40	2.5 7.5 12.5 17.5 22.5 27.5 32.5 37.5	2 5 7 13 21 16 8 3	5 37.5 87.5 227.5 472.5 440 260 112.5	19.4 14.4 9.4 4.4 0.6 5.6 10.6 15.6	376.36 207.36 88.36 19.36 0.36 31.36 112.36 243.36	752.72 1036.8 618.52 251.68 7.56 501.76 898.88 730.08
		Σf = 75	Σfm = 1642.5			Σfx2 = 4798

$$\begin{gathered} \overline{\mathit{X}}=\frac{\mathrm{\Sigma }fm}{\mathrm{\Sigma }f}=\frac{1642.5}{75}=21.9 \\ SD=\sqrt{\frac{\mathrm{\Sigma }f{x}^2}{\mathrm{\Sigma }f}}=\sqrt{\frac{4798}{75}}=\sqrt{63.97}=7.99 \\ \mathrm{Variance}\left({\sigma }^2\right)=\frac{\mathrm{\Sigma }f{x}^2}{\mathrm{\Sigma }f}=\frac{4798}{75}=63.97 \end{gathered}$$