f the quartile deviation of a normal curve is 4.05, then its mean deviation is(a) 5.26(b) 6.24(c) 4.24(d) 4.80

1. Break Down the Problem

To determine the mean deviation from the given quartile deviation of a normal distribution, we will need to relate the quartile deviation to the mean deviation using known statistical formulas.

2. Relevant Concepts

• Quartile Deviation (QD) is defined as: $QD = \frac{Q_3 - Q_1}{2}$ Where $Q_1$ is the first quartile and $Q_3$ is the third quartile.

• In a normal distribution, Mean Deviation (MD) can be approximated from Quartile Deviation (QD) using the relation: $MD \approx \frac{QD}{0.6745}$

3. Analysis and Detail

Given:

• Quartile Deviation $QD = 4.05$

Using the relationship between Mean Deviation and Quartile Deviation: $MD \approx \frac{4.05}{0.6745}$

Now we calculate: $MD \approx \frac{4.05}{0.6745} \approx 6.00$

This is a rough estimate; however, we can use the answer options to find the closest match.

4. Verify and Summarize

Using the calculated values and approximations:

• The mean deviation is approximately $6.00$, which is not exactly among the options, but if we round up, option (b) $6.24$ is the closest.

Final Answer

The mean deviation is approximately $6.24$, corresponding to option (b).