Data

Unit Review Sheet

Facts and Definitions

Lesson 1: Statistics Review

• A measure of center is a number that identifies the center value of a distribution.
• The mean of a data set is the average of all the data values in the set.
• $\mathrm{Mean}=\frac{\mathrm{Sum\; of\; all\; values}}{\mathrm{Number}of\mathrm{values}}$
• The median is the middle value in a data set that is arranged in order from smallest to largest.
• To find the median of a data set with an even number of values, add the two middle numbers and divide the sum by 2.
• The mode of a data set is the value that occurs the most frequently.
• Mean, median, and mode are measures of center.
• Variability describes how spread out or different the numbers in a data set are.
• The range is the difference between the largest and the smallest values in a data set.
• The interquartile range (IQR) measures how spread out the middle 50% of a data set is.
• $\mathrm{IQR}=Q_3-Q_1$
• The mean absolute deviation (MAD) measures how far, on average, each data value is from the mean.
• $\mathrm{MAD}=\frac{\mathrm{sum}of\mathrm{absolute}differencesfromthe\mathrm{mean}}{\mathrm{number}of\mathrm{data}values}$
• A box plot is a graph that shows the center and spread of a data set using five key numbers: minimum, maximum, median, first quartile, and third quartile.
• In a box plot the rectangle always shows the middle 50% of the data set.

Lesson 2: Scatterplots

• A scatter plot is a graph of plotted points that shows the relationship between two sets of data.
• A linear relationship occurs when two variables show a pattern that forms a straight line on a scatterplot.
• A positive linear relationship means that the variables move in the same direction. As x is increasing, y is also increasing.
• A negative linear relationship means that the variables move in the opposite direction. As x is increasing, y is decreasing.
• When points are scattered randomly on a scatterplot, the variables have no relationship.
• A cluster is a group of data points that are close together.
• An outlier is a data point that is separated from the rest of the points.
• On a scatterplot, a trend is the general direction in which data points move.
• A best fit line is a straight line that shows the overall trend in a scatterplot.
• High variability means the points are widely scattered around the best fit line, showing a weaker relationship between the variables.
• Low variability means the points cluster closely around the best fit line, showing a stronger relationship between the variables.
• Correlation means two things change together.
• Causation means a change in one variable influences a change in the other variable.

Lesson 3: Constructing a Scatter Plot

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Lesson 4: Linear Models

• A linear model is a straight‑line equation that shows how two things are connected. It helps predict what will happen next by showing how much the dependent variable ($y$) changes whenever the independent variable ($x$) changes.
• Slope means how much $y$ changes compared to how much $x$ changes.

Lesson 5: Categorical Data

• Categorical Data is data that can be sorted into named groups based on shared qualities (ex: color, type of pet, or zip code).
• Numerical Data refers to data that represents measurable quantities or amounts (ex: height, money, or temperature).
• A two‑way frequency table is a table that displays data for two categorical variables at the same time. Each cell represents the frequency of cases that fall into both categories.
• A two-way relative frequency table shows the proportions or percentages of data in each category instead of raw counts.

Lesson 6: Unit 8 Test

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Final Project: Collecting and Organizing Data

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