Question

Find mean of the following frequency table:

Hint:

For grouped data, use class mid-points as $x_i$ and remember the compact formula $\ \bar{x}=\dfrac{\sum f_ix_i}{\sum f_i}$. The assumed-mean or step-deviation methods speed this up when numbers are large.

Answer 1

 

Step 1: Find class marks (mid-points)
$0$–$6\Rightarrow x_1=\dfrac{0+6}{2}=3$; $6$–$12\Rightarrow x_2=9$; $12$–$18\Rightarrow x_3=15$; $18$–$24\Rightarrow x_4=21$; $24$–$30\Rightarrow x_5=27$.
 

Step 2: Use $\bar{x}=\dfrac{\sum f_ix_i}{\sum f_i}$
$\sum f_i=5+9+10+12+4=40$.
$\sum f_ix_i=5(3)+9(9)+10(15)+12(21)+4(27)$
$\hspace{2.8cm}=15+81+150+252+108=606$.
 

Step 3: Compute the mean
\[ \bar{x}=\frac{\sum f_ix_i}{\sum f_i}=\frac{606}{40}=15.15. \] \[ \boxed{\text{Mean }=15.15} \]