QA 5

Flashcards covering key concepts of Descriptive Statistics, focusing on Measures of Central Tendency including mean, median, mode, trimmed mean, and weighted average, as well as their properties and appropriate uses.

What is the main purpose of Descriptive Statistics?

To describe the main characteristics or features of a dataset, such as its mean, median, mode, or standard deviation.

What is the difference between a population parameter and a descriptive statistic (sample statistic)?

A population parameter quantitatively describes a characteristic of data from a population (e.g., population mean μ), while a descriptive statistic quantitatively describes a characteristic of data from a sample (e.g., sample mean x̄).

What do measures of central tendency describe?

They describe the central value, location, or a typical value of a distribution.

How is the arithmetic mean calculated?

The arithmetic mean is calculated by summing all values in a dataset and dividing by the total number of observations (sum of all values / number of observations).

How are outliers related to the arithmetic mean?

The arithmetic mean is sensitive to extreme values (outliers), meaning outliers can significantly affect its value.

How is the median calculated for a simple distribution?

To find the median, first place all values in order from smallest to largest. Then, locate the value at the median position, which is (n+1)/2, where n is the number of observations.

How do outliers affect the median?

The median is not significantly affected by extreme values or outliers, making it useful for skewed distributions.

What is the mode of a distribution?

The mode is the value that occurs most frequently in a distribution. A distribution can have no mode, one mode, or several modes.

When is the trimmed mean used?

The trimmed mean is used when there are outliers in the data; it removes a percentage of the smallest and largest values before calculating the mean to reduce the influence of these extremes.

What is the purpose of a weighted average?

A weighted average is used when some numbers in a dataset need to be assigned more importance or 'weight' than others. It's calculated as the sum of (value × weight) divided by the sum of weights.

Which measure of central tendency is most appropriate for nominal data?

The mode is generally the most appropriate measure of central tendency for nominal data.

Which measure(s) of central tendency are resistant to outliers?

The mode, median, and trimmed mean are resistant to extreme values because they are not affected much by outliers in a data set.

How do the mean, median, and mode relate in a left-skewed distribution?

In a left-skewed distribution, the mean is typically less than the median, which is less than the mode (Mean < Median < Mode).

How do the mean, median, and mode relate in a right-skewed distribution?

In a right-skewed distribution, the mean is typically greater than the median, which is greater than the mode (Mean > Median > Mode).

How do the mean, median, and mode relate in a symmetric distribution?

In a symmetric distribution, the mean, median, and mode are approximately equal (Mean = Median = Mode).