SAT Math15 cards

Data Analysis Flashcards

Data Analysis covers the statistics and probability concepts tested on the SAT Math section. This topic includes measures of central tendency, spread, probability calculations, interpreting scatterplots and tables, linear regression, and working with ratios and percentages.

All 15 Flashcards

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What is the mean of a data set?

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The sum of all values divided by the number of values.

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What is the median of a data set?

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The middle value when data is ordered. For an even count, average the two middle values.

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What is the mode?

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The value that appears most frequently in a data set. A set can have no mode or multiple modes.

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How does an outlier affect the mean vs. the median?

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Outliers pull the mean toward them significantly but have little effect on the median. Use median for skewed data.

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What is standard deviation?

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A measure of how spread out values are from the mean. Larger standard deviation = more spread.

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What is the range of a data set?

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Maximum value minus minimum value.

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How do you calculate the probability of a single event?

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P(event) = number of favorable outcomes / total number of possible outcomes.

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What is the probability of two independent events both occurring?

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Multiply their individual probabilities: P(A and B) = P(A) * P(B).

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What does a line of best fit represent on a scatterplot?

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The linear equation that best approximates the trend in the data, minimizing the overall distance from each point to the line.

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In the regression equation y = ax + b, what does 'a' represent?

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The slope: the predicted change in y for each one-unit increase in x.

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What does a correlation coefficient (r) close to 1 or -1 indicate?

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A strong linear relationship. Positive r = positive association, negative r = negative association, r near 0 = weak/no linear trend.

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How do you convert a percentage to a decimal?

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Divide by 100. For example, 35% = 0.35.

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How do you calculate percent change?

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((New - Original) / Original) * 100%.

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What is a ratio, and how do you use it to find actual quantities?

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A ratio compares parts (e.g., 3:5). If the total is 40, each 'part' = 40/8 = 5, giving quantities of 15 and 25.

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How do you read a two-way frequency table?

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Rows and columns represent categories. Cell values are counts. Use row/column totals to calculate conditional probabilities or percentages.

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Study Tips for Data Analysis

1

When a problem says 'average' it almost always means the arithmetic mean. Read carefully to check if it asks for median or mode instead.

2

For probability questions involving 'or,' add the probabilities and subtract the overlap: P(A or B) = P(A) + P(B) - P(A and B).

3

On scatterplot problems, always read the axis labels and units before interpreting the slope or making predictions. Misreading units is a common trap.

4

Practice percent change problems with real numbers first. The SAT often embeds these in word problems about price increases, population changes, or survey results.

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