Question

The marks obtained out of 50, by 102 students in a physics test are given in the frequency table below:
Marks (x): 15 20 22 24 25 30 33 38 45
Frequency (f): 5 8 11 20 23 18 13 3 1

Find the average number of marks..

Answer 1

ASSUMED MEAN METHOD :  

In this method, first of all, one among xi 's is chosen as the assumed mean denoted  by ‘A’. After that the difference ‘di’ between ‘A’ and each of the xi's i.e di = xi - A is calculated .  

ARITHMETIC MEAN =  A +  Σfidi / Σfi

[‘Σ’ Sigma means ‘summation’ ]

★★ We may take Assumed mean 'A’ to be that xi which lies in the middle of x1 ,x2 …..xn.

FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT  

From the table : Σfidi = 110 ,Σfi = 102 ,  

Let the assumed mean, A = 25

ARITHMETIC MEAN =  A +  Σfidi / Σfi

ARITHMETIC MEAN =  25 + (110/102)

= 25 + 55/51

= 25 + 1.078

= 26.078

ARITHMETIC MEAN = 26.078 ≈ 26.08 (approximate)  

Hence, the average number of marks is ≈ 26.08(approximate).  

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

15+20+22+24+25+30+33+38+45/9
252/9
28 is the answer