Final answer:
A standard unit measures how many standard deviations an observation is from the mean, indicating the spread of data around the average. The Empirical Rule tells us that in a normal distribution, about 68% of observations lie within one standard deviation of the mean. Option A
Step-by-step explanation:
A standard unit measures how many standard deviations away an observation is from the mean. In other words, it measures how many units of the standard deviation a particular observation is from the average value of the data.
For example, if an observation falls exactly at the mean of a dataset, it is 0 standard deviations away. If it is one standard deviation above the mean, it is said to be at the +1 standard deviation mark, and so forth.
The magnitude of the standard deviation itself tells us about the spread of data. If data points are closely clustered around the mean, the standard deviation will be small, indicating low variability.
Conversely, if data points are spread out over a wider range of values, the standard deviation will be larger, indicating greater variability. The concept of standard deviation is crucial in statistics as it provides a measurable way to determine how much variation exists within a set of data.
Using the Empirical Rule, we understand that for a normal distribution, roughly 68% of the observations fall within one standard deviation of the mean. This is a very important concept in descriptive statistics and helps to understand the distribution of data. Option A