Understanding Data Distribution Shapes

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Questions and Answers

Which of the following describes a symmetrical data distribution?

The mean, median, and mode are equal. (correct)
More than half of the scores are below the peak.
There is a long tail of values below the peak.
The mean is less than the median.

In a positively skewed data set, the mean is less than the median.

False (B)

What is the relationship between the mean, median, and mode in a positively skewed distribution?

mode < median < mean or mean > median > mode

A distribution where scores are evenly spread around a central value is called a __________ distribution.

normal Signup and view all the answers

Match the following terms with their definitions:

Mean = The average of a data set Median = The middle value of a data set Mode = The most frequently occurring value in a data set Skew = The measure of asymmetry in a distribution Signup and view all the answers

Which measure of central tendency is not equal in a positively skewed distribution?

Mean (D) Signup and view all the answers

A normal distribution is an example of asymmetrical data.

False (B) Signup and view all the answers

What term describes a data set that has a long tail of values above the peak of the graph?

skew Signup and view all the answers

In a symmetrical distribution, roughly ______% of scores will be above and below the mean.

50 Signup and view all the answers

Match each type of distribution with its characteristics:

Symmetrical = Mean = Median = Mode Positive skew = Mean > Median > Mode Normal distribution = Bell-shaped curve Asymmetrical = Not evenly spread around a central value Signup and view all the answers

Flashcards

Symmetrical Data

Data distribution where values are evenly spread around the central point, with an equal number of values above and below the mean.

Skewness

A measure of how symmetrical or asymmetrical a distribution is. It indicates the direction and extent of the data's imbalance.

Positive Skew

Data distribution with a long tail extending to the right (higher values) of the peak. The mean is greater than the median, which is greater than the mode.

Mode

The most frequent value in a dataset. In symmetrical data, it coincides with the mean and median. In positively skewed data, it's the smallest of the three measures of central tendency.

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Median

The middle value when data is arranged in order. In symmetrical data, it coincides with the mean and mode. In positively skewed data, it's between the mean and mode.

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Symmetrical Distribution

A distribution where values are evenly spread around the center. The mean, median, and mode are equal.

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Negative Skew

A distribution with a longer tail extending towards lower values. Mean < Median < Mode.

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Study Notes

Describing Data Shape

Data distribution shape is analyzed for symmetry and asymmetry.
Measures of central tendency—median, mean, and mode—are crucial for understanding skew.
Symmetry: Data is symmetrical if it's centered around a central value without bias toward either left or right. Approximately 50% of scores fall above the mean, and 50% below.
Normal distribution is a symmetrical data example. The normal distribution is perfectly symmetrical; mean, median, and mode are equal.
Histograms effectively illustrate symmetrical distributions. A symmetrical distribution's histogram visually shows a mirroring effect.
Asymmetry/Skew: Data is asymmetrical (skewed) if it isn't symmetrical.
Positive Skew (Right Skew): Data with a longer tail to the right; more than half of the scores are above the peak. This results in mean > median > mode.