Question

If the mean of the following data is 14.7, find the value of p and q.
class frequency
0-6 10
6-12 p
12-18 4
18-24 7
24-30 q
30-36 4
36-42 1
Total 40

Answer 1

The value of p = 11 and q is 3.

Explanation:

Given table :

class   frequency        Class mark      

                 f                     x                          xf

0-6          10                     3                           30

6-12          p                     9                             9p

12-18         4                    15                            60    

18-24         7                      21                        147          

24-30         q                    27                        27q                  

30-36         4                     33                       132            

36-42          1                    39                           39      

Total         26+p+q                                          $\sum xf=$  408 +9p +27q

$\sum f =40$  (given)

So ,   26+p+q  =40

⇒p+q = 14          --------------(1)

Mean = $\dfrac{\sum xf}{\sum f}$    [We are given mean = 14.7]

$14.7=\dfrac{408 +9p +27q}{40}\\\\ 408 +9p +27q=588\\\\ 9p +27q=180\\\\ p+3q=20----(2)$  

Subtract (1) from (2) , we get

$2q=6\\\\ q=3$

Put value of q in (1) , we get p=11

Hence, the value of p = 11 and q is 3.

# Learn  more :

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Answer 2

p = 11 ; q = 3

Step-by-step explanation:

Please find the attached a picture of the table showing the class, frequency and fx. The answer is with respect to the attached picture only.

Given sum of frequency = 40

26 + p + q = 40

p + q = 14 ---------------(1)

Given Mean = 14.7

Mean = sum of fx / sum of f

14.7 = (408 + 9p + 27q) / 40

588 = 408 + 9p + 27q

180 = 9p + 27q

Cancelling by 9 on both sides, we get:

p + 3q = 20 --------------- (2)

Subtracting (1) from (2), we get:

2q = 6

So q = 3

Substituting q = 3 in equation 1, we get:

p = 14-3

So p = 11

Hence solved.