The mean of the following data is 21.6. Find the value of p.

xi	fi
6	5
12	4
18	p
24	6
30	4
36	6

Mean = $\dfrac{\sum f$ixi}{\sum f_i}

∑f_i = 5 + 4 + p + 6 + 4 + 6 = 25 + p

∑f_ix_i​ = 30 + 48 + 18p + 144 + 120 + 216 = 558 + 18p

⇒ 21.6 = $\dfrac{558+18p}{25+p}$

⇒ 21.6(25 + p) = 558 + 18p

⇒ 540 + 21.6p = 558 + 18p

⇒ 21.6p − 18p = 558 − 540

⇒ 3.6p = 18

⇒ p = $\dfrac{18}{3.6}$ = 5

Hence, p = 5.