5 Descriptive Statistics Free Online FlashCards

How do nominal and ordinal categories differ?

Nominal categories have no natural order; ordinal categories have a meaningful order.

What does a category's relative frequency represent?

Relative frequency is a category's count divided by the total number of observations; it gives the category's share of the data.

What is the mode?

The mode is the most frequent category or value.

Why is a histogram unsuitable for nominal categories?

A histogram's numerical bins imply intervals, which nominal categories do not have. Use a bar chart instead.

How is the mean calculated?

The mean is the sum of all observations divided by their number: $\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i$.

How do you find the median with an even number of observations?

Sort the observations and average the two middle values.

How can an extreme observation affect the mean?

Because the mean uses every observation, an unusually high or low value can pull it toward the tail.

How is the range calculated?

The range is the maximum value minus the minimum value.

What does the interquartile range measure?

The IQR is $Q_3-Q_1$; it describes the spread of the middle half of the data and is relatively resistant to extremes.

What is the usual formula for sample variance?

For a sample, variance is the sum of squared deviations from the mean divided by $n-1$: $s^2=\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}$.

How does standard deviation relate to variance and measurement units?

Standard deviation is the square root of variance, so it describes spread in the data's original units.

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

For roughly symmetric data without strong outliers, use mean and standard deviation; for skewed data or extreme values, median and IQR are often more representative.