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Algebra 1 Unit 8: Data & statistics

Statistics in Algebra 1 is about summarizing data and describing relationships between two variables.

Covers: Mean, median, mode and range, box plots and IQR, scatterplots and correlation, lines of best fit, two-way tables

Study guide

Statistics describes data. Measures of center include the mean (average), the median (middle of sorted data), and the mode (most common value). The range (max − min) is a simple measure of spread. The median resists outliers, while the mean is pulled toward them.

A box plot shows the five-number summary: minimum, first quartile (Q1), median, third quartile (Q3) and maximum. The interquartile range, IQR = Q3 − Q1, is the spread of the middle half of the data. Values more than 1.5·IQR below Q1 or above Q3 are usually called outliers.

Scatterplots show two quantitative variables. Positive association means y tends to increase as x increases; negative association means it tends to decrease. The correlation coefficient r measures the strength and direction of a linear relationship, from −1 to 1. Correlation does not prove causation: a third factor can cause both.

A line of best fit summarizes a linear trend. Its slope is the predicted change in y per unit of x, and its y-intercept is the predicted y when x = 0. Residuals (actual − predicted) show how far points fall from the line. Two-way tables show counts for two categorical variables; relative frequencies (row or column percentages) let you compare groups fairly.

Standard deviation measures how far data values typically lie from the mean; a larger value means the data are more spread out. When comparing two data sets, compare means for center and standard deviations for consistency, and use a calculator to compute them. To find a regression line, enter the data into two lists and run linear regression, then round a and b as instructed and write y = ax + b. A value of r close to 1 or −1 shows a strong linear relationship, its sign gives the direction, and a value near 0 shows a weak one.

To find quartiles, sort the data and find the median. Q1 is the median of the lower half and Q3 is the median of the upper half, leaving out the overall median if the number of values is odd.

Key ideas

• Mean = sum ÷ count; median = middle value; mode = most common.
• Range = max − min; IQR = Q3 − Q1.
• Scatterplots show positive, negative or no association.
• A line of best fit's slope is the predicted change in y for each unit of x.
• Correlation doesn't prove causation.

Formulas and rules

Common mistakes

• Forgetting to sort data before finding the median.
• Calling a correlation proof that one variable causes the other.

Words to know

Median

The middle value of sorted data.

IQR

Q3 − Q1, the spread of the middle half.

Positive association

As x increases, y tends to increase.

Slope of a best-fit line

Predicted change in y for each one-unit increase in x.

Correlation vs. causation

Correlation shows a relationship, not that one variable causes the other.

Mean

The average: sum of values ÷ number of values.

Mode

The most common value.

Range

Maximum − minimum.

Box plot

Shows the minimum, Q1, median, Q3 and maximum.

Outlier

A value far from the rest, often beyond 1.5·IQR from the quartiles.

Correlation coefficient (r)

Measures a linear relationship's strength and direction, from −1 to 1.

Residual

Actual − predicted value.

Two-way table

Counts for two categorical variables; relative frequencies compare groups.

Sample practice questions

29 more questions like these, from level 1 to 5, are in the practice set.