If the mean of the following data is 8- find the value of p- - x 3 5 7 9 11 13- f 6 8 15 p 8 4- -

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Standard X

Mathematics

Direct Method of Finding Mean

If the mean o...

Question

If the mean of the following data is 8, find the value of p.
$\begin{matrix} x & 3 & 5 & 7 & 9 & 11 & 13 f & 6 & 8 & 15 & p & 8 & 4 \end{matrix}$

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Solution

We prepare the following frequency table:

(xi) (fi) xifi

3 6 18

5 8 40

7 15 105

9 p 9p

11 8 88

13 4 52

Σfi=41+p Σfixi= 303+9p

Mean =

Σfixi=303+9p

Σfi=41+p

But, mean = 8 (given)

Thus, we have:
$8 = \frac{303 + 9 p}{41 + p}$
⇒ $328 + 8 p = 303 + 9 p$

⇒ $p = 25$

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(xi)	(fi)	xifi
3	6	18
5	8	40
7	15	105
9	p	9p
11	8	88
13	4	52
	Σfi=41+p	Σfixi= 303+9p

If the mean of the following data is 8, find the value of p. x35791113f6815p84

We prepare the following frequency table: (xi) (fi) xifi 3 6 18 5 8 40 7 15 105 9 p 9p 11 8 88 13 4 52 Σfi=41+p Σfixi= 303+9p Mean = Σfixi=303+9p Σfi=41+p But, mean = 8 (given) Thus, we have: 8=303+9p41+p ⇒328+8p=303+9p ⇒p=25

If the mean of the following data is 8, find the value of p.
$\begin{matrix} x & 3 & 5 & 7 & 9 & 11 & 13 f & 6 & 8 & 15 & p & 8 & 4 \end{matrix}$

We prepare the following frequency table:

(xi) (fi) xifi

3 6 18

5 8 40

7 15 105

9 p 9p

11 8 88

13 4 52

Σfi=41+p Σfixi= 303+9p

Mean =

Σfixi=303+9p

Σfi=41+p

But, mean = 8 (given)

Thus, we have:
$8 = \frac{303 + 9 p}{41 + p}$
⇒ $328 + 8 p = 303 + 9 p$

⇒ $p = 25$