AP®︎ Statistics: Topic 1.7 Flashcards

Master key terms and definitions for Topic 1.7 of AP Statistics – Summary Statistics for One Quantitative Variable to help you prep for quizzes and the AP exam.

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Term

Statistic vs. Parameter

Definition

A statistic summarizes a sample; a parameter summarizes an entire population

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Statistic vs. Parameter
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A statistic summarizes a sample; a parameter summarizes an entire population

1.7.A
Sample Mean (x̄)
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Arithmetic average of sample values: x̄ = (Σx_i)/n

1.7.A1.7.A.2
Median
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Middle value of an ordered data set; for even n, commonly the mean of the two middle values

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Minimum
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Smallest value in an ordered data set

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Maximum
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Largest value in an ordered data set

1.7.A1.7.A.4
Quartiles (Q1, Q2, Q3)
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Values that divide ordered data into four parts: Q1 is the median of the lower half, Q2 is the median, and Q3 is the median of the upper half; Q1 and Q3 bound the middle 50%

1.7.A1.7.A.5
Percentile
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The pth percentile is the value with approximately p% of the ordered data at or below it

1.7.A1.7.A.6
Range
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Maximum − minimum

1.7.B1.7.B.2
Interquartile Range (IQR)
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Q3 − Q1; the spread of the middle 50% of the data

1.7.B1.7.B.3
Sample Standard Deviation (s)
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Typical distance of sample values from their mean; s = sqrt(Σ(x_i − x̄)² / (n − 1))

1.7.B1.7.B.4
Sample Variance (s²)
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The square of the sample standard deviation: s² = Σ(x_i − x̄)² / (n − 1); measured in squared units

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Resistant (Robust) Statistic
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A statistic not greatly affected by outliers or extreme values; median and IQR are resistant

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Nonresistant (Non-Robust) Statistic
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A statistic that can be changed substantially by outliers or extreme values; mean, range, and standard deviation are nonresistant

1.7.F1.7.F.1
Mean and Standard Deviation vs. Median and IQR
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Use mean and standard deviation for reasonably symmetric data without strong outliers; use median and IQR for skewed data or data with outliers

1.7.F1.7.F.1
1.5 × IQR Rule
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A value is a potential outlier if it is below Q1 − 1.5(IQR) or above Q3 + 1.5(IQR)

1.7.D1.7.D.1.i
Two-Standard-Deviation Rule
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A value is a potential outlier by this rule if it is below x̄ − 2s or above x̄ + 2s

1.7.D1.7.D.1.ii
Linear Change of Units
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If y = a + bx, then mean, median, quartiles, percentiles, minimum, and maximum change by a + b(original); range, IQR, and standard deviation are multiplied by |b|; variance is multiplied by b²

1.7.C1.7.C.1
Lower Fence and Upper Fence
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Lower fence = Q1 − 1.5(IQR); upper fence = Q3 + 1.5(IQR); values below/above them are potential outliers by the 1.5 × IQR rule

1.7.D1.7.D.1.i