Describing the Distribution of Quantitative Variables - AP Statistics

1. What does the range of a data set describe?

   The difference between the maximum and minimum values. Calculated as max - min, showing the total spread of values.

2. Identify one advantage of using a histogram.

   Shows the shape of the data distribution. Visual pattern reveals skewness, modality, and spread characteristics.

3. Find the range of the data set: 10, 15, 20, 25, 30.

   20. Maximum value (30) minus minimum value (10) equals 20.

4. Identify the term for data represented by a single peak.

   Unimodal. Distribution has exactly one peak or mode.

5. Which term describes a distribution with a longer right tail?

   Right-skewed. The tail extends toward higher values, creating positive skew.

6. State the formula for calculating the variance of a data set.

   $\frac{\sum (x_i - \bar{x})^2}{n-1}$. Average of squared deviations from the mean, using n-1 denominator.

7. What is the term for the spread of data around the mean?

   Standard deviation. Square root of variance, measuring typical deviation from mean.

8. What does a box plot visually represent?

   The five-number summary. Box shows quartiles and whiskers extend to min/max values.

9. What graphical display is best for showing data distribution?

   Histogram. Shows frequency distribution using bars for different value ranges.

10. State the formula for calculating the mean of a data set.

    $\frac{\sum x_i}{n}$. Sum all values and divide by the number of observations.

11. Identify the characteristics of a normal distribution shape.

    Symmetrical and bell-shaped. Data clusters around the center with equal tails on both sides.

12. Choose the term that describes the peak of a distribution.

    Mode. The mode represents the highest point or most common value.

13. What is a characteristic of a uniform distribution?

    All values have approximately the same frequency. Each outcome occurs with roughly equal probability or frequency.

14. Which term describes a distribution with a longer left tail?

    Left-skewed. The tail extends toward lower values, creating negative skew.

15. Identify the measure of center that is the middle value.

    Median. When data is ordered, this value sits exactly in the center position.

16. Calculate the range of the data set: 8, 3, 5, 12.

    9. Maximum value (12) minus minimum value (3) equals 9.

17. What does the interquartile range measure?

    The spread of the middle 50% of data. IQR = Q3 - Q1, showing variability in the central portion of data.

18. What is the purpose of a stem-and-leaf plot?

    To display data while retaining original values. Preserves actual data values unlike histograms that group data.

19. What is the term for the average of the squared deviations?

    Variance. Standard deviation squared, measuring spread around the mean.

20. Which measure of spread is most resistant to outliers?

    Interquartile Range (IQR). IQR only uses middle 50% of data, ignoring extreme outliers.

21. Identify the term for a data point significantly different from others.

    Outlier. Values that fall unusually far from the typical data pattern.

22. Which measure is used to describe the center of skewed data?

    Median. Median resists outlier influence better than mean in skewed data.

23. What is the term for the most frequent value in a data set?

    Mode. The value that appears most often in the data set.

24. What does a negatively skewed distribution indicate?

    Mean < Median. Left tail pulls mean lower than the median value.

25. What is the five-number summary of a data set?

    Minimum, Q1, Median, Q3, Maximum. These five values completely describe the data's position and spread.

26. What does a positively skewed distribution indicate?

    Mean > Median. Right tail pulls mean higher than the median value.

27. Find the median of the data set: 3, 5, 7, 9, 11.

    7. The middle value when 3, 5, 7, 9, 11 are arranged in order.

28. What is the mode of the data set: 4, 4, 5, 6, 7?

    4. The value 4 appears most frequently in this data set.

29. Which measure of center is affected by extreme values?

    Mean. Outliers pull the mean toward them, making it sensitive to extreme values.

30. Identify the term for the spread of the entire data set.

    Range. Measures the distance between maximum and minimum data values.

31. Find the mean of the data set: 2, 4, 6, 8.

    5. Sum is 20, divided by 4 observations gives mean of 5.

32. What is the definition of a quantitative variable?

    A variable that can be measured numerically. Unlike categorical variables, these have numerical values that can be calculated.

33. Identify the first step in creating a box plot.

    Calculate the five-number summary. Min, Q1, median, Q3, and max are needed for the box plot structure.

34. What is the definition of the standard deviation?

    A measure of the amount of variation in a data set. Measures how much individual values deviate from the mean on average.

35. What is the shape of a distribution with two peaks called?

    Bimodal. Distribution has exactly two distinct peaks or modes.

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