4 Descriptive Statistics Free Online FlashCards

What do descriptive statistics summarize?

Descriptive statistics summarize observed data, such as its typical values, variation, positions, and relationships. They do not by themselves establish causes or population-wide patterns.

How is the mean calculated?

The mean is the sum of all values divided by their number: $\bar{x}=\frac{\sum x_i}{n}$.

How do you find the median?

The median is the middle value after the data are ordered. With an even number of values, it is the average of the two middle values.

What is the mode?

The mode is the most frequent value. A distribution may have more than one mode, or none that is useful.

How is the range calculated, and what is one limitation?

The range is the maximum value minus the minimum value: $\text{range}=\max-\min$. It depends only on the two extremes.

What does the interquartile range measure?

The interquartile range is $Q_3-Q_1$. It describes the span of the middle half of the data and is less sensitive to extremes than the range.

How do the usual sample and population variance denominators differ?

Variance is the average squared distance from the mean. Sample variance divides the squared deviations by $n-1$; population variance divides by $N$.

What does standard deviation describe, and in what units?

Standard deviation is the square root of the variance. It describes spread around the mean and is expressed in the data’s original units.

Which center-and-spread pairs suit symmetric and skewed data?

Use the mean and standard deviation for a reasonably symmetric distribution without influential outliers; use the median and IQR for skewed data or data with outliers.

What positions do $Q_1$, the median, and $Q_3$ represent?

Quartiles divide ordered data into four parts: $Q_1$ is the 25th percentile, the median is the 50th, and $Q_3$ is the 75th.

What does a z-score express?

A z-score gives a value’s distance from the mean in standard-deviation units: $z=\frac{\text{value}-\text{mean}}{\text{standard deviation}}$. A score of $-1$ is one standard deviation below the mean.

What should you inspect in a scatterplot of two quantitative variables?

For two quantitative variables, use a scatterplot to inspect direction, form, strength, clusters, and unusual points before interpreting a summary.