Question

Find the missing value of p for the following distribution whose mean is 12.58
x:
5
8
10
12
p
20
25
f:
2
5
8
22
7
4
2

Answer 1

ARITHMETIC MEAN OR MEAN OR AVERAGE :  

The arithmetic mean of a set of observations is obtained by dividing the sum of the values of all observations by the total number of observations .

Mean = Sum of all the observations / Total number of observations .

MEAN = Σfixi / Σfi

[‘Σ’ Sigma means ‘summation’ ]

FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT  

From the table : Σfixi = 524 + 7p , Σfi = 50

MEAN = Σfixi / Σfi  

Given : Mean = 12.58  

12.58   = (524 + 7p) / 50

12.58 × 50 =  (524 + 7p)  

629 = (524 + 7p)

7p = 629 - 524  

7p = 105

p = 105/7 = 15

p = 15

Hence, the value of ‘p’ is 15.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer:

Step-by-step explanation:

sigma(x*f(x)) : (5*2)+(8*5)+(10*8)+(12*22)+(p*7)+(20*4)+(25*2)

                  = 10+40+80+264+7p+80+50

                  = 524+7p

sigma f(x)  : 2+5+8+22+7+4+2

                = 50

mean = sigma(x*f(x)) / sigma f(x)  = 524+7p / 50  = 12.58

                                                 = 524 + 7p = 12.58 * 50

                                                 = 7p = 629-524

                                                      p = 15