Unit 1: Exploring One-Variable Data (copy)

What is a categorical variable?

A variable that takes on values that are category names or group labels.

How can categorical variables be represented?

They can be organized into frequency tables, relative frequency tables, or displayed graphically using bar graphs, dot plots, and pie charts.

What is the relative frequency of parents wanting the school year to be 180 days?

55% of parents expressed a desire for the school year to be 180 days.

What is the difference between discrete and continuous quantitative variables?

Discrete variables take on a countable number of values with gaps between them, whereas continuous variables can take on an infinite number of values with no gaps.

What is the median?

The middle number of a set of numbers arranged in numerical order.

What does a bimodal distribution indicate?

A distribution with two distinct peaks or clusters.

How do you calculate the interquartile range (IQR)?

By subtracting the first quartile (Q1) from the third quartile (Q3).

What does a positive z-score represent?

A value that is above the mean.

What does it mean if a distribution is skewed to the right?

It spreads far and thinly toward the higher values, with the mean usually greater than the median.

What is the empirical rule in statistics?

The rule stating that for a normal distribution, about 68% of the values lie within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean.

What are two ways of denoting the mean of a distribution?

The population mean is denoted by µ (mu) and the sample mean by x̄.

What is variability in statistics?

Variability refers to how much the data points differ from each other, a key concept in understanding data.

What does a right-skewed distribution imply about the median and mean?

In a right-skewed distribution, the mean is usually greater than the median.

What is the range of a data set?

The difference between the largest and smallest values in a data set.

How are summary statistics represented graphically?

They can be displayed using boxplots, histograms, or cumulative frequency plots.

What is the typical distance each value is from the mean called?

Standard deviation.

What kind of distribution is described by a histogram that is symmetric and bell-shaped?

A normal distribution.

How do you interpret the median and interquartile range from historical population data?

Comparing medians and IQRs can indicate changes in population age demographics over time.

In the context of a normal distribution, what can be concluded about taxicab mileage in NYC based on the empirical rule?

Approximately 68% of taxis are driven between 63,000 and 87,000 miles annually.