Data Vocabulary

Question 1

Association

Answer 1

A connection between data values.

Question 2

Bivariate data

Answer 2

Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team.

Question 3

Box Plot

Answer 3

A method of visually displaying a distribution of data values by using the median, quartiles, and extremes of the data set. A box shows the middle 50% of the data.

Question 4

Box-and-Whisker Plot

Answer 4

A diagram that shows the five-number summary of a distribution. (Five-number summary includes the minimum, lower quartile (25th percentile), median (50th percentile), upper quartile (75th percentile), and the maximum. In a modified box plot, the presence of outliers can also be illustrated.

Question 5

Categorical Variables

Answer 5

Categorical variables take on values that are names or labels. The color of a ball (e.g., red, green, blue), gender (male or female), year in school (freshmen, sophomore, junior, senior). These are data that cannot be averaged or represented by a scatter plot as they have no numerical meaning.

Question 6

Center

Answer 6

Measures of center refer to the summary measures used to describe the most “typical” value in a set of data. The two most common measures of center are median and the mean.

Question 7

Conditional Frequencies

Answer 7

The relative frequencies in the body of a two-way frequency table.

Question 8

Correlation Coefficient

Answer 8

A measure of the strength of the linear relationship between two variables that is defined in terms of the (sample) covariance of the variables divided by their (sample) standard deviations.

Question 9

Dot plot

Answer 9

A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line.

Question 10

First Quartile

Answer 10

(Q1) The “middle value” in the lower half of the rank-ordered data

Question 11

Five Number Summary

Answer 11

Minimum, lower quartile, median, upper quartile, maximum.

Question 12

Histogram

Answer 12

Graphical display that subdivides the data into class intervals and uses a rectangle to show the frequency of observations in those intervals—for example you might do intervals of 0-3, 4-7, 8-11, and 12-15

Question 13

Interquartile Range

Answer 13

A measure of variation in a set of numerical data. The interquartile range is the distance between the first and third quartiles of the data set. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the interquartile range is 15 – 6 = 9.

Question 14

Joint Frequencies

Answer 14

Entries in the body of a two-way frequency table.

Question 15

Line of Best Fit

Answer 15

A straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points. Remind students that an exponential model will produce a curved fit. (also called trend or regression line).

Question 16

Marginal Frequencies

Answer 16

Entries in the “Total” row and “Total” column of a two-way frequency table.

Question 17

Mean Absolute Deviation

Answer 17

A measure of variation in a set of numerical data, computed by adding the distances between each data value and the mean, then dividing by the number of data values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean absolute deviation is 20.

Question 18

Outlier

Answer 18

Sometimes, distributions are characterized by extreme values that differ greatly from the other observations. These extreme values are called outliers. As a rule, an extreme value is considered to be an outlier if it is at least 1.5 interquartile ranges below the lower quartile (Q1), or at least 1.5 interquartile ranges above the upper quartile (Q3).
OUTLIER if the values lie outside these specific ranges:
Q1 – 1.5 • IQR
Q3 + 1.5 • IQR

Question 19

Quantitative Variables

Answer 19

Numerical variables that represent a measurable quantity. For example, when we speak of the population of a city, we are talking about the number of people in the city – a measurable attribute of the city. Therefore, population would be a quantitative variable. Other examples: scores on a set of tests, height and weight, temperature at the top of each hour.

Question 20

Residuals

Answer 20

Represents unexplained (or residual) variation after fitting a regression model. residual = observed value – predicted value e = y – ŷ. A residual plot is a graph that shows the residual values on the vertical axis and the independent (x) variable on the horizontal axis.

Question 21

Scatter plot

Answer 21

A graph in the coordinate plane representing a set of bivariate data. For example, the heights and weights of a group of people could be displayed on a scatter plot. If you are looking for values that fall within the range of values plotted on the scatter plot, you are interpolating. If you are looking for values that fall beyond the range of those values plotted on the scatter plot, you are extrapolating.

Question 22

Second Quartile

Answer 22

(Q2) The median value in the data set.

Question 23

Shape

Answer 23

The shape of a distribution is described by symmetry, number of peaks, direction of skew, or uniformity.

Question 24

Symmetry

Answer 24

A symmetric distribution can be divided at the center so that each half is a mirror image of the other.

Question 25

Number of Peaks

Answer 25

Distributions can have few or many peaks. Distributions with one clear peak are called unimodal and distributions with two clear peaks are called bimodal. Unimodal distributions are sometimes called bell-shaped.

Question 26

Direction of Skew

Answer 26

Some distributions have many more observations on one side of graph than the other. Distributions with a tail on the right toward the higher values are said to be skewed right; and distributions with a tail on the left toward the lower values are said to be skewed left.

Question 27

Uniformity

Answer 27

When observations in a set of data are equally spread across the range of the distribution, the distribution is called uniform distribution. A uniform distribution has no clear peaks.

Question 28

Spread

Answer 28

The spread of a distribution refers to the variability of the data. If the data cluster around a single central value, the spread is smaller. The further the observations fall from the center, the greater the spread or variability of the set. (range, interquartile range, Mean Absolute Deviation, and Standard Deviation measure the spread of data)

Question 29

Third quartile

Answer 29

For a data set with median M, the third quartile is the median of the data values greater than M. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the third quartile is 15.

Question 30

Trend

Answer 30

A change (either positive, negative or constant) in data values over time.

Question 31

Two-Frequency Table

Answer 31

A useful tool for examining relationships between categorical variables. The entries in the cells of a two-way table can be frequency counts or relative frequencies.