Question

Candidate of our school appear in a mathematics test. The data were as follows:
Schools:
I
II
III
IV
No.of candidates
60
48
not available
40
Average Score
75
80
55
50
If the average score of the candidates of all the four schools is 66, find the number of candidates that appeared from school III

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  

Let the  number of candidate that appeared from school III be x .  

From the table : Σfixi = 10340 + 55x  , Σfi = 260

MEAN = Σfixi / Σfi  

Given : Average score (Mean) = 66

66 = 10340 + 55x/ 260  

66 × 260 = 10340 + 55x

17160 = 10340 + 55x

55x = 17160 - 10340

55x = 6820

x = 6820/55 = 124

x = 124  

Hence,the  number of candidate that appeared from school III is 124 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Let Number of. candidates appeared

from school III = p

Mean = Σfixi/Σfi = 66 [ Given ]

=> ( 10340 + 55p )/( 148 + p ) = 66

=> 10340 + 55p= 66( 148 + p )

=> 10340 + 55p = 9768 + 66p

=> 10340 - 9768 = 66x - 55p

=> 572 = 11p

=> ( 572/11 ) = p

=> 52 = p

p = 52

Therefore ,

Number of candidates that appeared

from school III = p = 52

••••