Question

The mean of the 10 observations 15,17,23,18,p,25,16,18,20,12, is 18.Find the value of p​

Answer 1

Given:-

• Mean = 18
• No. of observations = 10
• Observations = 15,17,23,18,p,25,16,18,20,12

Solution :-

⇒ Mean = sum of observations/ number of observations

⇒ 18 = 15+17+23+18+p+25+16+18+20+12 / 10

⇒ 180 = 164 + p

⇒ p = 180 - 164

⇒ p = 16

Therefore, the value of p is 16.

More to know:-

⇒ Formula for mean of grouped data:-

• Direct method,

Mean = Σfi xi / ΣfI

• Assumed mean method,

Mean = a + Σfi di/Σfi

• Step deviation method,

Mean = a + (Σfi ui/Σfi) × h

Answer 2

$\large\underline\blue{\bold{Given \:  Question :-  }}$

• The mean of the 10 observations 15,17,23,18,p,25,16,18,20,12, is 18. Find the value of p

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$\huge \orange{AηsωeR} ✏$

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$\begin{gathered}\begin{gathered}\bf Given - \begin{cases} &\sf{number \: of \: observations \: = 10} \\ &\sf{mean \: of \: 10 \: observations \: = 18}\\ &\sf{15,17,23,18,p,25,16,18,20,12} \end{cases}\end{gathered}\end{gathered}$

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$\begin{gathered}\begin{gathered}\bf To \: Find :- \begin{cases} &\sf{value \: of \: p} \end{cases}\end{gathered}\end{gathered}$

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$\large\underline\purple{\bold{Solution :- }}$

$\begin{gathered}\begin{gathered}\bf \begin{cases} &\sf{number \: of \: observations \: = 10} \\ &\sf{mean \: of \: 10 \: observations \: = 18}\\ &\sf{observations \: are \: 15,17,23,18,p,25,16,18,20,12} \end{cases}\end{gathered}\end{gathered}$

$\bf \:  ✏We \: know, \: mean \: is \: given \: by$

$\bf \:  ⟼{\overline x } = \dfrac{\bf \sum_{i=1}^n\bf {x _i} }{n}$

$\sf \:  ⟼18 = \dfrac{15 + 17 + 23 + 18 + p + 25 + 16 + 18 + 20 + 12}{10}$

$\sf \:  ⟼180 = p + 164$

$\bf\implies \:p \: = \: 16$

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