Quartile Deviation:

The quartile deviation is a statistical measure that provides an indication of the spread or dispersion of a dataset. It is calculated as half the difference between the first and third quartiles. The first quartile (Q1) is the value below which 25% of the data falls, and the third quartile (Q3) is the value below which 75% of the data falls.

Given Information:

- Mean (μ) = 10
- Standard Deviation (σ) = 4

Finding the Quartiles:

To find the quartiles, we will use the properties of a normal distribution. In a normal distribution, the first quartile is located approximately 0.6745 standard deviations below the mean, and the third quartile is located approximately 0.6745 standard deviations above the mean.

Calculating the First Quartile (Q1):

Q1 = μ - (0.6745 * σ)
= 10 - (0.6745 * 4)
= 7.702

Calculating the Third Quartile (Q3):

Q3 = μ + (0.6745 * σ)
= 10 + (0.6745 * 4)
= 12.798

Calculating the Quartile Deviation:

Quartile Deviation = (Q3 - Q1) / 2
= (12.798 - 7.702) / 2
= 2.548

Therefore, the quartile deviation of the given normal distribution is approximately 2.548.

Answer:

None of the options (a), (b), (c), or (d) matches the calculated quartile deviation of 2.548.