Question

Find the value of p, if the mean of the following distribution is 7.5
x:3,5,7,9,11,13
f:6,8,15,p,8,4
(A) 6
(B)4
(C)2
(D)3​

Answer 1

$\huge\sf\red{Answer:}$

⇒ Option - D (3)

Step-By-Step-Explanation:

★ Given question:

⇒ Find the value of p, if the mean of the following distribution is 7.5 x: 3,5,7,9,11,13 f: 6,8,15,p,8,4.

⇒ $\sf Σfi = 41+p$

⇒ $\sf Σfixi = 303+9p$

⇒ $\sf Mean = \dfrac{Σfixi}{Σfi}$

⇒ $\sf 7.5 = \dfrac{(303+9p)}{ (41 +p)}$

⇒ $\sf 7.5 (41 +p) = 303 +9p$

⇒ $\sf [(307.5 + 7.5 \: p)= (303 + 9p)]$

⇒ $\sf [(307.5 - 303) = (9p - 7.5 \: p)]$

⇒ $\sf 4.5 = 1.5 \: p$

⇒ $\sf p = \dfrac{4.5}{1.5} = 3$

⇒ ${\sf{\underline{\boxed{\green{\sf{p = 3 }}}}}}$

Hence, 3 is the the value of p.

★ NOTE:

☆ Refer the attachment for thr table.