6 Descriptive Statistics Free Online FlashCards

What does frequency measure?

A frequency is the number of times a value or category appears in a data set.

How is relative frequency calculated?

Relative frequency is the category’s frequency divided by the total number of observations: $\frac{f}{n}$. Relative frequencies sum to $1$, or $100\%$, aside from rounding.

What does cumulative frequency tell you?

Cumulative frequency is the running total of counts up to and including a value. It shows how many observations are at or below that value.

What is the trade-off when numerical data are grouped into intervals?

Grouping values into intervals can make patterns easier to see, but it hides the exact values within each interval.

How is the arithmetic mean calculated?

Add all values and divide by their count: $\bar{x}=\frac{\sum x_i}{n}$. For a frequency table, weight each value by its frequency before dividing by the total frequency.

How is the median found?

Sort the observations. With an odd count, the median is the middle value; with an even count, it is the average of the two middle values.

What is the mode?

The mode is the most frequently occurring value or category. A data set can have several modes or no mode if no value occurs more often than the others.

How can an extreme high value affect the mean and median?

An extreme high value can pull the mean upward, while the median is often less affected and can better represent the center of skewed data.

How is the range calculated, and what does it depend on?

The range is the largest value minus the smallest value: $\text{range}=\max(x)-\min(x)$. It depends only on those two extremes.

What does the interquartile range measure?

The interquartile range is $\text{IQR}=Q_3-Q_1$. It describes the spread of the middle half of the data and is less affected by extremes than the range or standard deviation.

What do $Q_1$ and $Q_3$ represent?

Quartiles divide ordered data into four parts. $Q_1$ is the 25th percentile and $Q_3$ is the 75th percentile; calculation conventions can differ, so state the convention when exact agreement matters.

How do the population and sample variance formulas differ?

Population variance divides squared deviations from the population mean by $N$: $\sigma^2=\frac{\sum(x_i-\mu)^2}{N}$. Sample variance divides squared deviations from the sample mean by $n-1$: $s^2=\frac{\sum(x_i-\bar{x})^2}{n-1}$.