Question

Find the value of p, if the mean of the following distribution is 20.
x:
15
17
19
20+p
23
f:
2
3
4
5p
6

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 = 295 + 5p(20 + p)  ,Σfi = 15 + 5p  

MEAN = Σfixi / Σfi  

Given : Mean = 20

20 = 295 + 5p(20 + p) / (15 + 5p)

20 × (15 + 5p) = 295 + 100p + 5p²

300 + 100p = 5p² + 100p + 295

5p² + 100p + 295 = 300 + 100p

5p² + 100p - 100p = 300 - 295

5p² = 5  

p² = 5/5 = 1

p² = 1

p = √1 = 1  

p = 1  

Hence, the value of p is 1 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

this is the answer you see it