Question

if the mean of the following distribution is 27 find the value of P
classes 0-10 10 - 20 20- 30 30 - 40 40-50
frequency 8 p 12 13 10​

Answer 1

   $\huge{\boxed{\sf{Answer}}}$

   STATISTIC PROBLEM : FIND THE VALUE OF " P ".

• There are three methods for solving the problems of Statistics :

    1) By Direct Method

    2) By Assumed mean method and

    3)  By Step derivation method

• Me is gonna to solve or find the value of "P" by

       " Step deviation method ".

Classes       Frequency ( fi )           xi                  ui = xi - a/h            fiui

 0-10                     8                           5                       -2                     -16

10-20                    P                          15                       -1                      -P

20-30                  12                     25 ⇒ ( a )               0                       0

30-40                  13                          35                        1                       13

40-50                  10                          45                        2                     20

                       _______                                                                  _______

                       ∑fi=43+P                                                               ∑fiui = 17-P

                   

xi = upper limit + lower line  

ui = xi - assumed mean ( a ) / h

h = upper limit - lower limit

  =  20 - 10 = 10

fiui = frequency given × ui

Formula : $\overline{x}$ = a + h { ∑fiui / ∑fi }

Given mean ($\overline{x}$) = 27

27 = 25 + 10 [ (17 - p) / (43 + p ) ]

27- 25  = 10 [ (17 - p) / (43 + p ) ]

2 / 10 = (17 - p) / (43 + p )

86 + 2p = 170 - 10 p

12 p = 84

P = 84 / 12

P = 7

Hence, the value of " P " = 7...

Answer 2

Answer..

7

0-10 8 5 -2 -16

10-20 P 15 -1 -P

20-30 12 25 ⇒ ( a ) 0 0

30-40 13 35 1 13

40-50 10 45 2 20

fi=43+P fiui = 17-P

xi = upper limit and

lower line

(ui = xi )( assumed mean ( a ) / h)

(h = upper limit (lower limit)

( 20 - 10 = 10)

frequency given × ui

Formula : \overline{x}

x

= a + h { ∑fiui / ∑fi }

Given mean (\overline{x} x ) = 27

27 = 25 + 10 [ (17 - p) / (43 + p ) ]

27- 25 = 10 [ (17 - p) / (43 + p ) ]

2 / 10 = (17 - p) / (43 + p )

86 + 2p = 170 - 10 p

12 p = 84

P = 84 / 12

P = 7