Extracting Information from Data - AP Computer Science Principles

1. Which central tendency measure is not affected by extreme values?

   Median. Position-based measure unaffected by outliers or extreme values.

2. What measure describes the amount of variation in a data set?

   Standard deviation. Measures how spread out the data points are from the mean.

3. What is the mode of the data set 1, 2, 2, 3, 4?

   The mode is 2. The value that appears most frequently in the data set.

4. Identify the median of the data set 2, 4, 6, 8, 10.

   The median is 6. The middle value when data is ordered from least to greatest.

5. What is the main advantage of using a line graph?

   Shows trends over time. Clearly displays changes and patterns in data over time periods.

6. What is the median of the data set 3, 7, 9, 12, 15?

   The median is 9. The middle value in the ordered data set of five values.

7. Identify the outlier in the data set 1, 2, 3, 100, 5.

   The outlier is 100. Value 100 is extremely different from the other small values.

8. What graphical representation uses bars to show frequency?

   Bar graph. Uses rectangular bars with heights representing data frequencies.

9. Calculate the mode of the data set 5, 5, 7, 9, 9.

   Modes are 5 and 9. Both values 5 and 9 appear twice, tied for highest frequency.

10. Find the mean of the data set 10, 20, 30, 40.

    The mean is 25. Sum all values and divide by count: $(10+20+30+40)/4 = 25$.

11. Find the mode of the data set 10, 10, 20, 30, 30.

    Modes are 10 and 30. Values 10 and 30 each appear twice, tied for most frequent.

12. What is the mean of the data set 3, 5, 7, 9, 11?

    The mean is 7. Sum all values and divide by count: $(3+5+7+9+11)/5 = 35/5 = 7$.

13. What type of chart is best for showing parts of a whole?

    Pie chart. Displays proportions as sections of a complete circle.

14. Identify the median of the data set 1, 3, 5, 7, 9.

    The median is 5. The middle value when five numbers are arranged in order.

15. Which measure of central tendency is most affected by outliers?

    Mean. Outliers heavily influence the mean since it uses all values in calculation.

16. Identify the mode of the data set 7, 8, 8, 9, 10.

    The mode is 8. The value 8 appears twice, more than any other value.

17. Calculate the mean of the data set 6, 8, 10, 12, 14.

    The mean is 10. Sum divided by count: $(6+8+10+12+14)/5 = 50/5 = 10$.

18. What type of data visualization uses sectors of a circle?

    Pie chart. Divides circle into sections representing data proportions.

19. Identify the range of the data set 1, 5, 9, 13, 17.

    The range is 16. Maximum minus minimum: $17 - 1 = 16$.

20. What is the first step in calculating the variance?

    Find the mean of the data set. Variance measures squared deviations from the mean.

21. What statistical measure represents the most frequent data point?

    Mode. Identifies the value that occurs with the highest frequency.

22. What is the standard deviation a measure of?

    It measures data spread from the mean. Quantifies how much individual values deviate from the average.

23. What is the formula for the interquartile range (IQR)?

    $\text{IQR} = Q_3 - Q_1$. Difference between the third quartile and first quartile values.

24. Identify the outlier in the data set 3, 4, 5, 100.

    The outlier is 100. Value 100 is extremely different from the other clustered values.

25. Which term describes a graphical representation of a frequency distribution?

    Histogram. Bar chart showing the frequency of data values or intervals.

26. What does a scatter plot represent?

    Relationship between two variables. Each point shows how two different variables relate to each other.

27. What is the formula for calculating the mean?

    $\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}}$. Add all data values and divide by the total number of values.

28. What does a histogram display?

    Frequency distribution of a data set. Shows how often each value or interval occurs in the data.

29. Calculate the median of the data set 5, 7, 9, 11, 13.

    The median is 9. The middle value when the five numbers are in order.

30. Calculate the range of the data set 2, 4, 6, 8, 10.

    The range is 8. Maximum minus minimum: $10 - 2 = 8$.

31. Calculate the range of the data set 5, 10, 15, 20.

    The range is 15. Difference between maximum and minimum: $20 - 5 = 15$.

32. Calculate the median of the data set 2, 4, 6, 8.

    The median is 5. Average of the two middle values: $(4+6)/2 = 5$.

33. What is the purpose of a bar graph?

    To compare quantities across categories. Uses bar heights to compare values across different categories.

34. What statistical measure is used to describe the center of a data set?

    Mean. Represents the typical or average value of the data set.

35. What does the interquartile range (IQR) measure?

    Spread of the middle 50% of data. Distance between the first and third quartiles of the data.

36. Which graph type is best for showing data trends over time?

    Line graph. Connects data points to show patterns and changes over time.

37. What is the primary purpose of a box plot?

    To show data distribution and outliers. Displays quartiles, median, and identifies potential outliers visually.

38. Find the range of the data set 4, 8, 12, 16, 20.

    The range is 16. Maximum minus minimum: $20 - 4 = 16$.

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