Stat, Chapter 2: Modeling Distributions of Data

Front

What is a Normal distribution?

Back

A Normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where the mean, median, and mode are all equal.

Front

What does the mean represent in a data set?

Back

The mean is the average value of a data set, calculated by summing all values and dividing by the number of values.

Front

What is standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean.

Front

What percentage of data falls within one standard deviation of the mean in a Normal distribution?

Back

Approximately 68% of the data falls within one standard deviation of the mean in a Normal distribution.

Front

What percentage of data falls within two standard deviations of the mean in a Normal distribution?

Back

Approximately 95% of the data falls within two standard deviations of the mean in a Normal distribution.

Front

What is the empirical rule?

Back

The empirical rule states that for a Normal distribution, about 68% of data falls within one standard deviation, 95% within two, and 99.7% within three standard deviations from the mean.

Front

How do you calculate the z-score?

Back

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What does a z-score indicate?

Back

A z-score indicates how many standard deviations an element is from the mean. A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.

Front

What is a density curve?

Back

A density curve is a graphical representation of the distribution of a continuous random variable, showing the probability of different outcomes.

Front

What is the median in a data set?

Back

The median is the middle value of a data set when the values are arranged in ascending order. If there is an even number of observations, the median is the average of the two middle values.