# In the formula x̄ = a + f_{i}d_{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_{i}d_{i} = 110, Σf_{i} = 50

Find the mean.

The formula of assumed mean method is

Assumed mean method = A + (Σf_{i}d_{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_{i}d_{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_{i}d_{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. . . . .

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