Normal distribution and Empirical Rule

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What is the Empirical Rule?

Back

The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Tags

CCSS.HSS.ID.A.4

Front

What does it mean if a histogram is left skewed?

Back

A left skewed histogram has a longer tail on the left side, indicating that the majority of the data points are concentrated on the right.

Front

What does it mean if a histogram is right skewed?

Back

A right skewed histogram has a longer tail on the right side, indicating that the majority of the data points are concentrated on the left.

Front

What percentage of data falls within two standard deviations in a normal distribution?

Back

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

Tags

CCSS.HSS.ID.A.4

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 means that the values tend to be close to the mean, while a high standard deviation means that the values are spread out over a wider range.

Front

How do you determine if data is normally distributed?

Back

Data can be assessed for normality using graphical methods like histograms or Q-Q plots, and statistical tests such as the Shapiro-Wilk test.

Tags

CCSS.7.SP.B.3

Front

What is the significance of the mean in a normal distribution?

Back

The mean is the central point of a normal distribution, where the highest frequency of data points occurs.

Tags

CCSS.HSS.ID.A.2

CCSS.6.SP.B.5D

Front

What does a box plot represent?

Back

A box plot visually represents the distribution of a dataset through its quartiles, highlighting the median, upper and lower quartiles, and potential outliers.

Tags

CCSS.HSS.ID.A.1

CCSS.6.SP.B.4

Front

What is the median in a dataset?

Back

The median is the middle value when the data points are arranged in ascending order. It divides the dataset into two equal halves.

Tags

CCSS.6.SP.B.5C