Quartile Deviation of a Normal Distribution

The quartile deviation is a measure of dispersion that is used to describe the degree of spread in a dataset. It is defined as half of the difference between the third and first quartiles of a dataset.

Mean and Standard Deviation of Normal Distribution

In a normal distribution, the mean and standard deviation are important parameters that describe the distribution. The mean represents the central tendency of the distribution, while the standard deviation represents the degree of spread around the mean.

Given a normal distribution with mean 10 and standard deviation 4, we can use these parameters to calculate the quartile deviation.

Calculating Quartile Deviation

To calculate the quartile deviation, we first need to find the first and third quartiles of the distribution.

- The first quartile (Q1) is the value that separates the bottom 25% of the data from the top 75%.
- The third quartile (Q3) is the value that separates the bottom 75% of the data from the top 25%.

To find these values, we can use the standard normal distribution table or a calculator.

Using a table, we can find that the z-score corresponding to the first quartile is -0.6745, and the z-score corresponding to the third quartile is 0.6745.

To find the actual values for Q1 and Q3, we can use the formula:

Q1 = mean - z * SD
Q3 = mean + z * SD

Substituting the values we have, we get:

Q1 = 10 - (-0.6745) * 4 = 12.698
Q3 = 10 + 0.6745 * 4 = 13.302

The quartile deviation is then calculated as:

QD = (Q3 - Q1) / 2
QD = (13.302 - 12.698) / 2 = 0.302

Therefore, the quartile deviation of the normal distribution with mean 10 and standard deviation 4 is 0.302.