Question

23] In the formula of finding mean by
direct method, fi =
​

Answer 1

Step-by-step explanation:

Mean (or average) of observations, as we know, is the sum of the values of all the observations divided by the total number of observations.

If x

1 , x 2 ,… x n , are observations with respective frequencies f 1 , f 2 ,, . . ., f n then this means observation x 1 , occurs f 1 times, x 2 , occurs f 2 , times, and so on. Now, the sum of the values of all the observations = f 1 x 1 + f 2 x 2 + . . . + f n x n , and the number of observations = f 1 + f 2 + . . . + f n .

f1 x1 + f2 x2 + . . . + fn xn

x = ---------------------------------

f1 + f2 + . . . + fn

This can be written in short way using Greek letter Σ

Σfi xi

x = ------

Σ fi

Example 1 :

Weight (in Kgs) 67 70 72 73 75

Number of students 4 3 2 2 1

Find the average weight.

Solution :

Weight (in kg)xi

Frequency (fi)

fixi

67

4

268

70

3

210

72

2

144

73

2

146

75

1

75

N=Σ fi = 12

Σ fixi = 843

Σfi xi 843

x = ------- = ------- = 70.25 kg

Σ fi 12