Introduction:
Quartile deviation and standard deviation are both measures of dispersion that are used to describe the spread of data. In some cases, the quartile deviation and standard deviation may be equal, particularly when dealing with a moderately sweet distribution.

What is Quartile Deviation?
Quartile deviation is a measure of dispersion that is based on the spread of the quartiles in a dataset. It is calculated as half the difference between the upper and lower quartiles (Q3 - Q1) and is denoted by QD.

What is Standard Deviation?
Standard deviation is a measure of dispersion that is based on the spread of the data points in a dataset. It is calculated as the square root of the variance and is denoted by σ.

Why can QD be equal to σ in a moderately sweet distribution?
When dealing with a moderately sweet distribution, the spread of the data points is not too great, and the quartiles are fairly evenly spaced. In this case, the quartile deviation (QD) can be equal to the standard deviation (σ). This occurs when the quartiles are located at approximately one standard deviation away from the mean.

Conclusion:
In conclusion, the quartile deviation and standard deviation are both measures of dispersion that can be used to describe the spread of data. In some cases, such as a moderately sweet distribution, the quartile deviation may be equal to the standard deviation. It is important to understand the differences between these measures and when to use them appropriately.