If two distributions have equal means, then

Options

A. The distributions with lesser S.D. is more consistent
B. The distributions with lesser S.D. is less consistent
C. Their C.V.'s will also have equal
D. None of these

Answer

To solve the question, we need to analyze the implications of two distributions having equal means and evaluate the provided options based on statistical principles.

### Step-by-Step Solution:

1. **Understanding the Problem**: We are given that two distributions have equal means. We need to evaluate four statements regarding these distributions.

2. **Coefficient of Variation (Cv)**: The coefficient of variation is a measure of relative variability. It is calculated using the formula:
\[ Cv = \frac{\sigma}{\text{mean}} \times 100 \]
where \(\sigma\) is the standard deviation.

3. **Applying the Equal Means Condition**: Since both distributions have equal means, we can denote the common mean as \( \mu \). Thus, we can express the coefficients of variation for both distributions as:
\[ Cv_1 = \frac{\sigma_1}{\mu} \times 100 \]
\[ Cv_2 = \frac{\sigma_2}{\mu} \times 100 \]

4. **Analyzing Standard Deviation**: The consistency of a distribution is often measured by its standard deviation. A lower standard deviation indicates that the data points are closer to the mean, suggesting higher consistency.

5. **Comparing Coefficient of Variation**: If one distribution has a lesser standard deviation than the other (i.e., \(\sigma_1 < \sigma_2\)), then:
\[ Cv_1 < Cv_2 \]
This means that the distribution with the lesser standard deviation is more consistent.

6. **Evaluating the Options**:
- **Option A**: "The distribution with lesser standard deviation is more consistent." - This is correct based on our analysis.
- **Option B**: "The distribution with lesser standard deviation is less consistent." - This is incorrect.
- **Option C**: "Their series will also have equal." - This is ambiguous and cannot be concluded from the given information.
- **Option D**: "None of these." - This is incorrect since we have identified Option A as correct.

7. **Conclusion**: The only correct statement is Option A.

### Final Answer:
The correct option is **A**: The distribution with lesser standard deviation is more consistent.