AP Statistics Flashcards: Summary Statistics For A Quantitative Variable

What this deck covers

This deck focuses on Summary Statistics For A Quantitative Variable, giving you a quick way to review the definitions, rules, and examples that matter most for AP Statistics.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Calculate the weighted mean for $x: 3, 5, 7$ with weights $2, 3, 5$.

Answer: $\bar{x}_w = 5.8$. $\frac{2(3) + 3(5) + 5(7)}{2+3+5} = \frac{58}{10} = 5.8$.

Flashcard 2: Find the z-score for $x = 10$ given $\bar{x} = 8$, $s = 2$.

Answer: $z = 1$. $z = \frac{10-8}{2} = 1$ standard deviation above mean.

Flashcard 3: What does a positive kurtosis indicate?

Answer: Heavier tails than a normal distribution. More extreme values in tails than normal distribution.

Flashcard 4: Determine the median of the dataset: $3, 1, 4, 1, 5$.

Answer: Median = 3. Ordered: $1, 1, 3, 4, 5$; middle value is $3$.

Flashcard 5: What is the definition of the median?

Answer: The median is the middle value of a dataset when ordered. For odd $n$, it's position $\frac{n+1}{2}$; for even $n$, average of middle two.

Flashcard 6: What is the formula for the weighted mean?

Answer: $\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}$. Each value is multiplied by its weight before averaging.

Flashcard 7: Determine the mode of the dataset: $2, 2, 3, 4, 4, 4, 5$.

Answer: Mode = 4. Value $4$ appears three times, more than any other.

Flashcard 8: Define kurtosis in statistics.

Answer: Kurtosis measures the 'tailedness' of the distribution. High kurtosis means heavy tails; low means light tails.

Flashcard 9: What is the formula for population variance?

Answer: $\sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2$. Average squared deviation from population mean using $N$.

Flashcard 10: State the formula for the z-score of a data point.

Answer: $z = \frac{x - \bar{x}}{s}$. Number of standard deviations a value is from the mean.

Flashcard 11: Find the variance for dataset: $1, 2, 3, 4, 5$.

Answer: $s^2 = 2.5$. Mean is $3$; variance is $\frac{10}{4} = 2.5$.

Flashcard 12: Identify the formula for coefficient of variation.

Answer: $CV = \frac{s}{\bar{x}} \times 100\%$. Relative variability as a percentage of the mean.

Flashcard 13: Define the term 'outlier' in statistics.

Answer: An outlier is a data point significantly different from others. Falls unusually far from other observations in the dataset.

Flashcard 14: What is the formula for the sample mean of a dataset?

Answer: $\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$. Sum all values and divide by sample size $n$.

Flashcard 15: What is skewness in a dataset?

Answer: Skewness measures asymmetry of the probability distribution. Positive skew has right tail; negative skew has left tail.

Flashcard 16: Identify the formula for variance of a sample.

Answer: $s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2$. Average squared deviation from sample mean using $n-1$.

Flashcard 17: Define the interquartile range (IQR).

Answer: IQR = Q3 - Q1. Distance between third quartile and first quartile.

Flashcard 18: Identify the formula for the sample standard deviation.

Answer: $s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}$. Square root of sample variance using $n-1$ in denominator.

Flashcard 19: Identify the formula for the sample covariance.

Answer: $s_{xy} = \frac{1}{n-1} \sum (x_i - \bar{x})(y_i - \bar{y})$. Measures how two variables change together linearly.

Flashcard 20: Find the percentile rank of $4$ in $1, 2, 4, 5, 6$.

Answer: 60th percentile. Three out of five values are below $4$.

Flashcard 21: Identify the IQR of the dataset: $1, 3, 3, 6, 7, 8, 9$.

Answer: IQR = 5. $Q^3 = 8$, $Q^1 = 3$, so $IQR = 8 - 3 = 5$.

Flashcard 22: What does a boxplot visually represent?

Answer: A boxplot displays the distribution through five-number summary. Shows quartiles, median, and potential outliers graphically.

Flashcard 23: Find the range of the dataset: $9, 4, 7, 2, 5$.

Answer: Range = 7. Maximum $9$ minus minimum $2$ equals $7$.

Flashcard 24: What is the definition of a percentile?

Answer: A percentile indicates the relative standing of a value in a dataset. Shows what percentage of data falls below a given value.

Flashcard 25: What is the median of $8, 3, 6, 7, 5$?

Answer: Median = 6. Ordered: $3, 5, 6, 7, 8$; middle value is $6$.

Flashcard 26: Calculate the range for $10, 15, 20, 25, 30$.

Answer: Range = 20. Maximum $30$ minus minimum $10$ equals $20$.

Flashcard 27: What is a histogram used for?

Answer: A histogram displays the frequency distribution of a dataset. Shows data distribution using bars for frequency counts.

Flashcard 28: Calculate the range for $10, 15, 20, 25, 30$.

Answer: Range = 20. Maximum $30$ minus minimum $10$ equals $20$.

Flashcard 29: Calculate the mean of the dataset: $2, 4, 6, 8, 10$.

Answer: $\bar{x} = 6$. Sum is $30$, divided by $5$ observations gives $6$.

Flashcard 30: What is the median of $8, 3, 6, 7, 5$?

Answer: Median = 6. Ordered: $3, 5, 6, 7, 8$; middle value is $6$.

Flashcard 31: Identify the IQR of the dataset: $1, 3, 3, 6, 7, 8, 9$.

Answer: IQR = 5. $Q^3 = 8$, $Q^1 = 3$, so $IQR = 8 - 3 = 5$.

Flashcard 32: State the formula for the population mean.

Answer: $\mu = \frac{1}{N} \sum_{i=1}^{N} x_i$. Sum all values and divide by population size $N$.

Flashcard 33: What is the skewness of a symmetric distribution?

Answer: Skewness = 0. Symmetric distributions have equal left and right tails.

Flashcard 34: Calculate the standard deviation of $4, 4, 4, 4, 4$.

Answer: $s = 0$. All values are identical, so no variability exists.

Flashcard 35: How is the range of a dataset calculated?

Answer: Range = Maximum value - Minimum value. Difference between highest and lowest values in the dataset.

Flashcard 36: What is the five-number summary in statistics?

Answer: Minimum, Q1, Median, Q3, Maximum. Five key values that describe a dataset's distribution.