Descriptive Statistics: Measures of Center, Data Types, and Calculator Methods

A set of practice flashcards covering descriptive statistics topics from the lecture notes: measures of center (mean, median, mode, midrange), data types (qualitative vs quantitative), frequency tables, weighted means, and calculator methods.

What is descriptive statistics?

Describes data by summarizing and displaying its features (e.g., measures of center, patterns) rather than making inferences.

What is inferential statistics?

Uses a sample to make inferences or generalizations about the population.

What is the mean?

The arithmetic average: sum of all data values divided by the number of data values (n for a sample).

Which symbol represents the sample mean?

X-bar (the X with a bar on top).

Which symbol represents the population mean?

Mu (μ).

What is the median?

The middle value when data are ordered; for odd n it’s the middle value, for even n it’s the average of the two middle values.

What is the mode?

The data value that occurs most often; may be none; can be bimodal or multimodal.

What is midrange?

The midpoint between the minimum and maximum: (min + max) / 2; not a robust measure of center.

When is the mean the best measure of center?

For quantitative data with no outliers.

When is the median the best measure of center?

When there are outliers or skew in the data; more robust to extreme values.

For qualitative (nominal) data, which measure of center is best?

The mode is the best (mean and median aren’t meaningful for categorical data).

What is a modal class?

In a frequency distribution, the class interval with the highest frequency.

What is a weighted mean?

A mean where data values have different weights; computed as sum(weighti × valuei) / sum(weight_i).

How does GPA illustrate a weighted mean?

Convert grades to points (A=4, B=3, C=2, D=1, F=0); multiply by course credits, sum, divide by total credits; retakes may replace the prior grade depending on policy.

What is the five-number summary?

Minimum, first quartile (Q1), median, third quartile (Q3), maximum.

Can you compute mean or median from qualitative (categorical) data?

No; qualitative data are categories. Only the mode is meaningful for such data.

How do you estimate the mean from a frequency table?

Use the class midpoints multiplied by their frequencies, sum these products, and divide by the total frequency (N).

What is a class midpoint?

The midpoint of a class interval; used to approximate data values in grouped data.

What is a TI calculator’s one-bar stat used for?

To compute descriptive statistics (mean, standard deviation, etc.) from a single data list (or with a frequency list) and obtain values like X-bar and the five-number summary.

What does the five-number summary output by calculators include?

Minimum, Q1, Median, Q3, Maximum.

What is the modal class in a frequency table?

The class interval with the highest frequency; indicates where the data are most concentrated.

How do outliers affect the mean versus the median?

Outliers pull the mean toward themselves; the median is more robust to outliers and skew.

What do N and n represent?

N is the population size; n is the sample size.

What are the weights in a weighted mean example?

Weights are factors like credit hours or importance; used to scale each data value's contribution to the mean.

What is the method to compute the mean from grouped data using midpoints?

Compute the midpoint of each class, multiply by its frequency, sum these products, then divide by the total frequency to get the mean.