In the formula `bar(x)=a+(sumf_(i)d_(i))/(sumf_(i))`
for finding the mean of grouped data `d_(i) 'S` and deviation 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

Explanation

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:
\[ \bar{x} = a + \frac{\sum f_i d_i}{\sum f_i} \]
where:
- \(\bar{x}\) is the mean of the grouped data,
- \(a\) is a constant (usually the assumed mean or the midpoint of the class),
- \(f_i\) is the frequency of each class,
- \(d_i\) is the deviation of the class midpoint from \(a\).

### Step-by-step Solution:

1. **Identify the Components**:
- Recognize that \(d_i\) represents the deviation of the class midpoints from the assumed mean \(a\).
- The deviations \(d_i\) can be calculated as \(d_i = x_i - a\), where \(x_i\) is the midpoint of the class.

2. **Calculate Class Midpoints**:
- For each class interval, calculate the midpoint \(x_i\). The midpoint can be calculated using the formula:
\[ x_i = \frac{\text{Lower limit} + \text{Upper limit}}{2} \]

3. **Calculate Deviations**:
- Once you have the midpoints, calculate the deviations \(d_i\) for each class:
\[ d_i = x_i - a \]

4. **Multiply Deviations by Frequencies**:
- For each class, multiply the deviation \(d_i\) by the corresponding frequency \(f_i\):
\[ f_i d_i \]

5. **Sum the Products**:
- Sum all the products \(f_i d_i\) to get \(\sum f_i d_i\).

6. **Sum the Frequencies**:
- Sum all the frequencies to get \(\sum f_i\).

7. **Substitute into the Formula**:
- Substitute the values of \(a\), \(\sum f_i d_i\), and \(\sum f_i\) into the formula:
\[ \bar{x} = a + \frac{\sum f_i d_i}{\sum f_i} \]

8. **Calculate the Mean**:
- Perform the calculations to find \(\bar{x}\), the mean of the grouped data.