Question

Students of your class obtained following marks in Statistics in the weekly test:

Marks	4	5	6	7	8
Number of Students	12	10	18	20	24

Calculate arithmetic mean using Direct and Short-cut Methods.

Answer 1

Marks (X)	Frequency (f)	fX	Deviation d = X − A (A = 6)	Multiplication of deviation and frequency (fd)
4 5 6(A) 7 8	12 10 18 20 24	48 50 108 140 192	−2 −1 0 1 2	−24 −10 0 20 48
	Σf = 84	ΣfX = 538		Σfd = −34 + 68 = 34

Calculation of mean by Direct method
$$\begin{gathered} \overline{X}=\frac{\Sigma fX}{\mathrm{\Sigma }f} \\ \mathrm{or},\overline{X}=\frac{538}{84} \\ \Rightarrow \overline{X}=6.40 \end{gathered}$$

Calculation of mean by short cut method
$$\begin{gathered} \overline{\mathit{X}}=\mathrm{A}+\frac{\mathit{\Sigma }\mathit{f}\mathit{d}}{\mathit{\Sigma }\mathit{f}} \\ \mathrm{or},\overline{X}=6+\frac{34}{84} \\ \mathrm{or},\overline{X}=6+0.40 \\ \Rightarrow \overline{X}=6.40 \end{gathered}$$

So, average statistics marks is 6.40.