Representing Data with Number Line Plots - Statistics and Probability

1. What is the interquartile range (IQR) in a box plot?

   $IQR = Q_3 - Q_1$. Measures spread of the middle 50% of data.

2. What is the standard outlier rule using the $IQR$?

   Outliers are $< Q_1 - 1.5(IQR)$ or $> Q_3 + 1.5(IQR)$. Values beyond 1.5 IQRs from quartiles are potential outliers.

3. Find the $IQR$ if $Q_1=12$ and $Q_3=20$.

   $8$. Apply formula: $IQR = Q_3 - Q_1 = 20 - 12 = 8$.

4. What is the interquartile range in terms of quartiles?

   $IQR = Q_3 - Q_1$. Measures middle 50% spread between 25th and 75th percentiles.

5. What must be true about bin widths in a typical histogram used for comparison?

   Bin widths should be equal so bar heights compare frequencies fairly. Equal widths ensure visual comparison of frequencies is valid.

6. Identify the bin frequency if a histogram bar for $[10,15)$ has height $7$.

   $7$ data values. Height directly represents count of values in that interval.

7. Which plot type is best for comparing medians and $IQR$ across groups quickly?

   Box plot. Compact display emphasizes quartiles for group comparisons.

8. Find the upper outlier cutoff if $Q_1=10$, $Q_3=18$, and $IQR=8$.

   $30$. Calculate: $Q_3 + 1.5 \times IQR = 18 + 1.5(8) = 18 + 12 = 30$.

9. What must be true about bin widths in a standard histogram?

   Bins are non-overlapping and have equal width across the graph. Equal-width bins ensure fair visual comparison of frequencies.

10. Find the $IQR$: If $Q_1 = 12$ and $Q_3 = 20$, what is $IQR$?

    $8$. $IQR = Q_3 - Q_1 = 20 - 12 = 8$.

11. Which plot uses contiguous bars to show counts in intervals on a number line?

    Histogram. Adjacent bars touch to show continuous data ranges.

12. Which plot type is usually best for large quantitative data sets to show overall shape?

    Histogram. Bins summarize patterns in large continuous datasets.

13. What does the area of a bar represent in a density histogram?

    The relative frequency (proportion) in that bin. Area = relative frequency when total area equals 1.

14. Identify the outlier cutoff: If $Q_3 = 18$ and $IQR = 4$, what is the upper fence?

    $Q_3 + 1.5(IQR) = 18 + 6 = 24$. Upper fence = $Q_3 + 1.5 \times 4 = 18 + 6 = 24$.

15. What is a dot plot (line plot) used for when representing numerical data on a number line?

    A plot using dots above values to show frequencies on a number line. Shows frequency distribution of individual values visually.

16. What does a gap between bars in a histogram usually indicate?

    A bin with frequency $0$ (no data values in that interval). No bar appears when zero values fall within that interval.

17. What does stacking dots at the same position mean in a dot plot?

    Multiple data points have the same value (higher frequency). Dots stack vertically when values repeat, showing frequency visually.

18. What is a histogram used to represent for quantitative data?

    Frequencies of data values grouped into equal-width intervals (bins). Groups continuous data into bins to show distribution patterns.

19. What is a bin (class interval) in a histogram?

    A numerical interval that groups data values for counting frequency. Groups consecutive values to count occurrences in ranges.

20. Choose the correct statement: In a histogram, do bars touch or have gaps for continuous data?

    Bars touch (no gaps) to represent continuous intervals. Adjacent bars show data is continuous, not discrete categories.

21. Identify the outlier cutoff: If $Q_1 = 10$ and $IQR = 6$, what is the lower fence?

    $Q_1 - 1.5(IQR) = 10 - 9 = 1$. Lower fence = $Q_1 - 1.5 \times 6 = 10 - 9 = 1$.

22. Identify the plot type that best shows individual repeated values clearly.

    Dot plot. Shows exact values and frequencies with stacked dots.

23. What does the height of a bar represent in a frequency histogram?

    The number of data values in that bin (the frequency). Height shows count of values falling within that bin's range.

24. What does each dot represent in a dot plot when no key or scale change is given?

    One data value (one observation) at that number line position. Standard convention: one dot = one data point unless specified.

25. What percentile corresponds to $Q_1$ in a box plot?

    The $25$th percentile. One-quarter of data values fall below this point.

26. What is the main purpose of a histogram when representing quantitative data?

    To show frequencies of data grouped into equal-width intervals (bins). Bins group continuous data to visualize distribution shape.

27. Which plot type is usually best for very small data sets where individual values matter most?

    Dot plot. Shows each value clearly when n is small.

28. What is a box plot (box-and-whisker plot) designed to display?

    The five-number summary: min, $Q_1$, median, $Q_3$, max. Summarizes data spread using five key positional values.

29. Identify the frequency: Values $3,4,4,5,5,5$ are plotted; how many dots are above $5$?

    $3$. Count occurrences: 5 appears three times in the list.

30. Identify the plot type that best shows overall shape for large data sets.

    Histogram. Bins group many values to reveal distribution patterns.

31. What does the height of a bar in a frequency histogram represent?

    The number of data values in that bin (frequency). Bar height counts how many data points fall within that bin's range.

32. What do the whiskers represent in a modified box plot (with outliers shown separately)?

    The smallest and largest non-outlier values (within $1.5(IQR)$). Whiskers extend to most extreme non-outlier values.

33. What is a dot plot (line plot) used to represent on a number line?

    A data set by placing one dot above each value on a number line. Each value gets one dot positioned at its location on the number line.

34. Identify the plot type that best compares medians and IQRs across groups.

    Box plot. Displays five-number summaries side-by-side for comparison.

35. What are the outlier cutoffs using the $1.5\times IQR$ rule?

    Less than $Q_1-1.5IQR$ or greater than $Q_3+1.5IQR$. Points beyond 1.5 times the IQR from quartiles are outliers.

36. What percentile corresponds to $Q_3$ in a box plot?

    The $75$th percentile. Three-quarters of data values fall below this point.

37. What does the length of the box in a box plot represent?

    The interquartile range, $Q_3 - Q_1$. Box spans from first to third quartile, showing middle 50%.

38. What is a box plot (box-and-whisker plot) designed to display for a data set?

    The five-number summary: min, $Q_1$, median, $Q_3$, max. Visualizes spread and center using key percentiles.

39. What does the median line inside a box plot represent?

    The $50$th percentile of the data (middle value). Divides data in half: 50% above and 50% below this value.

40. Identify the median location: In a box plot, what does the line inside the box represent?

    The median (the $50$th percentile) of the data. Divides data into two equal halves by count.

Study these flashcards