Question

select the correct answer.

which assumption will work best for a large data set with a normal distribution?

most of the data points are close to the minimum value of the set.
most of the data points are close to the maximum value of the set.
most of the data points are close to the mean value of the set.
the data points are distributed uniformly over the range of the set.

Explanation:

Analyze the properties of a normal distribution

A normal distribution is a symmetric, bell-shaped curve where the highest frequency of data points occurs at the center.

Evaluate the location of the center

The center of a normal distribution is defined by its mean, median, and mode, which are all equal. Therefore, the density of data points is highest near the mean value.

Compare the given options

• Option 1 suggests clustering near the minimum, which describes a skewed distribution.
• Option 2 suggests clustering near the maximum, which also describes a skewed distribution.
• Option 3 states that most data points are close to the mean, which perfectly matches the bell-shaped characteristic.
• Option 4 describes a uniform distribution, not a normal distribution.

Answer:

• Most of the data points are close to the minimum value of the set.
• Most of the data points are close to the maximum value of the set.
• Most of the data points are close to the mean value of the set. (Correct answer)
• The data points are distributed uniformly over the range of the set.