In the formula x̄ = a + f_id_i/f_i for finding the mean of grouped data di ’s are deviations from a of
a. lower limits of the classes
b. upper limits of the classes
c. mid points of the classes
d. frequencies of the class marks

Solution:

In the formula given

\(\overline{x}=a+\frac{f_{i}d_{i}}{f_{i}}\)

a is the assumed mean from the class mark xi

d_i = x_i - a

x_i is the data

di is the deviation of class mark (mid value) from the assumed mean ‘a’

Therefore, di’s are deviations from ‘a’ of mid points of the classes.

✦ Try This: While calculating the mean of a given data by the assumed-mean method,the following values were obtained:

A = 25, Σf_id_i = 110, Σf_i = 50

Find the mean.

The formula of assumed mean method is

Assumed mean method = A + (Σf_id_i/ Σf_i)

Substituting the values

= 25 + (110/50)

By further calculation

= 25 + 2.2

= 27.2

Therefore, the mean is 27.2

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 14

NCERT Exemplar Class 10 Maths Exercise 13.1 Problem 1

In the formula x̄ = a + f_id_i/f_i for finding the mean of grouped data di ’s are deviations from a of a. lower limits of the classes, b. upper limits of the classes, c. mid points of the classes, d. frequencies of the class marks

Summary:

In the formula x̄ = a + f_id_i/f_i, for finding the mean of grouped data di ’s are deviations from a of mid points of the classes

☛ Related Questions:

• While computing mean of grouped data, we assume that the frequencies are a. evenly distributed over . . . .
• If xi ’s are the mid points of the class intervals of grouped data, fi ’s are the corresponding freq . . . .
• In the formula x̄ = a + h fi ui/ fi, for finding the mean of grouped frequency distribution, ui = a. . . . .