Choose the correct answer from the given four options:
In the formula `x=a+(sumx_(1)d_(i))/(sumf_(i))` for finding the mean of grouped data `d_(i)` 's are the deviations from a of

Options

A. lower limits of the classes
B. upper limits of the classes
C. mid-points of the classes
D. frequencies of the class marks

Answer

To solve the question regarding the formula for finding the mean of grouped data, we need to understand the components of the formula:

The formula given is:
\[ x = a + \frac{\sum (x_i d_i)}{\sum f_i} \]

Where:
- \( x \) is the mean of the grouped data.
- \( a \) is the assumed mean (or a base value).
- \( d_i \) are the deviations from \( a \).
- \( f_i \) are the frequencies of the classes.

### Step-by-Step Solution:

1. **Identify the components of the formula**:
- The formula consists of the assumed mean \( a \), the deviations \( d_i \), and the frequencies \( f_i \).

2. **Understanding deviations \( d_i \)**:
- The deviations \( d_i \) are calculated as \( d_i = x_i - a \), where \( x_i \) is the midpoint of each class interval.

3. **Determine what \( d_i \) represents**:
- Since \( d_i \) is defined as the difference between the midpoint of the class (\( x_i \)) and the assumed mean (\( a \)), it indicates that \( d_i \) represents the deviation of the midpoints from the assumed mean.

4. **Select the correct option**:
- The question asks what \( d_i \) represents in the context of the formula. The options provided are:
1. Lower limit of the class
2. Upper limit of the class
3. Midpoint of the classes
4. Frequencies of the class marks
- Since we established that \( d_i \) is derived from the midpoints of the classes, the correct answer is option 3: **Midpoint of the classes**.

### Final Answer:
The correct answer is: **Midpoint of the classes**.

---