Question

The frequency distribution dta is given below. If the average age is 17 yrs, the value of 'm' is Age (in yrs.): 8 20 26 29
no. of people: 3 2 m 1
​

Answer 1

AnswEr :

$\begin{tabular}{|c|c|c|c|c|}\cline{1-2}\cline{1-3}\cline{1-5}Age(In Yrs) & 8 & 20 & 26 & 29 \\\cline{1-5}No. of People&3&2&m&1&\cline{1-5}\cline{1-5}\end{tabular}$

$\rule{150}{1}$

$\begin{array}{|c|c|c|}\cline{1-3}\sf Age\:(x_i)&\sf No.\:of\:People\:(f_i) &\sf f_ix_i\\\cline{1-3}8&3&24\\20&2&40\\26&\sf m&\sf 26m\\29&1&29\\\cline{1-3} \sf Total&\sf f_{i}=(6+m)&\sf f_{i}x_{i}=(93+26m)\\\cline{1-3}\end{array}$

$\rule{200}{2}$

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$:\implies\tt Average= \dfrac{Sum\:of\:Terms}{Number\:of\:Terms}\\\\\\:\implies\tt 17 \:years =\dfrac{f_ix_i}{f_i} \\\\\\:\implies\tt 17 = \dfrac{93 + 26m}{6 + m}\\\\\\:\implies\tt 17(6 + m) = 93 + 26m\\\\\\:\implies\tt 102 + 17m = 93 + 26m\\\\\\:\implies\tt 102 - 93 = 26m - 17m\\\\\\:\implies\tt 9 = 9m\\\\\\:\implies\tt\dfrac{9}{9} = m\\\\\\:\implies\tt m = 1$

⠀

$\therefore\:\underline{\textsf{Hence, the value of m will be \textbf{1.}}}$

Answer 2

Answer:

=> Average = Sum/ Number

=> 17 = (93 + 26m)/ (6 + m)

=> 17(6 + m) = 93 + 26m

=> 102 + 17m = 93 + 26m

=> - 9m = - 9

=> m = 1