If mean deviation is 36, then the value of standard deviation will be ? (a) 45 (b) 35 (c) 25 (d) 15

To solve this problem, we need to establish the relationship between the mean deviation and the standard deviation. The mean deviation (also known as the mean absolute deviation) and the standard deviation are both measures of variability in a dataset, but they are calculated differently. 

### Relationship between Mean Deviation and Standard Deviation

The standard deviation is generally larger than the mean deviation for the same dataset. However, there is no fixed mathematical relationship between the mean deviation and the standard deviation because they measure spread differently. To answer this question correctly, we need more information about the distribution of the data, such as whether it's normal, uniform, etc. 

But if we assume the data follows a normal distribution (as is often the case in such problems unless otherwise stated), there's a rule of thumb:

\[
\text{Mean Deviation (MD)} \approx \frac{4}{5} \times \text{Standard Deviation (SD)}
\]

Given:
\[
\text{MD} = 36
\]

Let's calculate the standard deviation (SD) using the approximate formula:

\[
36 \approx \frac{4}{5} \times \text{SD}
\]

Solving for SD:

\[
\text{SD} \approx \frac{36 \times 5}{4}
\]

\[
\text{SD} \approx \frac{180}{4}
\]

\[
\text{SD} \approx 45
\]

### Conclusion

The value of the standard deviation is approximately **45**.

**Answer: (a) 45**

Would you like more details on the calculations, or do you have any other questions?

### Related Questions

1. What is the difference between mean deviation and standard deviation?
2. How do you calculate the mean deviation for a dataset?
3. When is it more appropriate to use standard deviation over mean deviation?
4. How does skewness affect the relationship between mean deviation and standard deviation?
5. Can you derive the standard deviation from variance?

**Tip:** Remember, standard deviation is more sensitive to outliers in the data compared to mean deviation.

Learn how to calculate the standard deviation from mean deviation with a step-by-step example problem. Understand the relationship between these two measures of variability in statistics. Suitable for high school students and anyone interested in statistical analysis.

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