Question

The following table gives the marks obtained by 10 students of a class:

S. No.	1	2	3	4	5	6	7	8	9	10
Marks	43	60	37	48	65	48	57	78	31	59

Find out mean marks, using Direct Method as well as Short-Cut Method

Answer 1

S.N.	Marks X	deviation from assumed mean (X − A)
1 2 3 4 5 6 7 8 9 10	43 60 37 48 $\boxed{65=A}$ 48 57 78 31 59	−22 −5 −28 −17 0 −17 −8 13 −34 −6
N=10	$\sum _{}\mathit{X}$=526	Σd=−124

(i) Calculating mean marks using direct method:

$$\begin{gathered} \overline{X}=\frac{{\displaystyle \sum _{}}X}{N} \\ \mathrm{or},\overline{X}=\frac{43+60+37+48+65+48+57+78+31+59}{10} \\ \mathrm{or},\overline{X}=\frac{526}{10} \\ \Rightarrow \overline{\mathrm{X}}=52.6marks \end{gathered}$$

(ii) Calculating mean marks using short cut method:

$\overline{X}=A+\frac{\Sigma d}{N}$
Here,
A represents assumed mean
d represents the deviation of the values from the assumed mean i.e. X − A

Here, we take 65 as the assumed mean. So, we take deviations of each item in the series from 65.

$$\begin{gathered} \overline{X}=65+\frac{(-124)}{10} \\ \mathrm{or},\overline{X}=65-\frac{124}{10} \\ \Rightarrow \overline{X}=52.6\mathrm{marks} \end{gathered}$$

Thus, mean marks is 52.6