Explanation:

Quartile deviation and standard deviation are measures of dispersion in a data set. Quartile deviation measures the spread of the middle 50% of the data while standard deviation measures the spread of the entire data set.

For a moderately non-symmetrical distribution, it is not necessary that Quartile deviation = Standard deviation /3. This statement is false.

Here are some reasons why this statement is false:

1. Non-symmetrical distributions may have different quartile deviations and standard deviations.

2. Quartile deviation is calculated based on quartiles, which divide the data into four equal parts. Standard deviation, on the other hand, is calculated based on the mean of the data.

3. The relationship between quartile deviation and standard deviation depends on the shape of the distribution. For symmetrical distributions, the quartile deviation is approximately equal to the standard deviation divided by 1.35. However, for non-symmetrical distributions, this relationship may not hold.

Therefore, the statement that Quartile deviation = Standard deviation /3 for a moderately non-symmetrical distribution is false.

Explanation:

Quartile deviation and standard deviation are two measures of dispersion used in statistics. Quartile deviation is the difference between the third and first quartiles, while standard deviation is the square root of the variance.

For a moderately non-symmetrical distribution, Quartile deviation is not equal to the standard deviation divided by 3. Therefore, option 'B' is the correct answer.

Here are some key points to keep in mind:

- Quartile deviation is a measure of dispersion that is based on the quartiles of a distribution. The first quartile is the value that separates the bottom 25% of the data from the top 75%, while the third quartile separates the bottom 75% from the top 25%.

- Standard deviation is a measure of dispersion that is based on the variance of a distribution. The variance is calculated by taking the average of the squared deviations from the mean, and the standard deviation is the square root of the variance.

- A moderately non-symmetrical distribution is one that is not perfectly symmetrical, but is not extremely skewed either. In such a case, the quartile deviation and standard deviation may be similar, but they are not equal.

- It is not true that Quartile deviation = Standard deviation /3 for a moderately non-symmetrical distribution. This statement is false and therefore, option 'B' is the correct answer.

- The relationship between quartile deviation and standard deviation depends on the shape of the distribution. For a perfectly symmetrical distribution, the quartile deviation is equal to the standard deviation divided by 1.35. For a positively skewed distribution, the quartile deviation is less than the standard deviation, while for a negatively skewed distribution, it is greater.

In conclusion, Quartile deviation is not equal to Standard deviation /3 for a moderately non-symmetrical distribution. Consequently, option 'B' is the correct answer.