Display Data in Statistical Plots - 6th Grade Math

1. Find $Q_1$ for the data set $[1,2,4,6,9,10,12,15]$.

   $3$. $Q_1$ is median of lower half: median of $[1,2,4,6]$ is $3$.

2. Identify $Q_3$ for the sorted data $\{1,2,4,7,9,10,11,12\}$ using the median-of-halves method.

   $10.5$. Median of upper half $\{9,10,11,12\}$ is $(10+11)/2$.

3. A box plot has minimum $2$, $Q_1 = 5$, median $7$, $Q_3 = 9$, maximum $12$. What is the range?

   $10$. Range = maximum - minimum = $12 - 2$.

4. What must be true about bin widths in a histogram for the display to be fair to compare bars?

   All bins must have the same width. Equal widths ensure fair visual comparison of frequencies.

5. Find $IQR$ for a box plot with $Q_1=5$ and $Q_3=13$.

   $8$. Apply formula: $IQR = Q_3 - Q_1 = 13 - 5 = 8$.

6. Identify the correct statement about the box in a box plot.

   The box spans from $Q_1$ to $Q_3$ (middle $50\%$ of data). Box contains the middle half of all data values.

7. Identify the best plot to show exact repetitions in this small data set: $[2,2,3,4,4,4]$.

   Dot plot. Dot plots clearly show individual values and repetitions.

8. What does it mean when dots are stacked above the same number in a dot plot?

   That value occurs multiple times (higher frequency). Stacking shows repeated values - more dots mean more occurrences.

9. In a box plot, what does the segment from $Q_1$ to $Q_3$ (the box) represent?

   The middle $50\%$ of the data (the IQR). The box contains the middle half of all data values.

10. What must be true about bin widths in a histogram for a fair display?

    All bins must have equal width. Equal widths ensure fair visual comparison between intervals.

11. What is the interquartile range (IQR) formula?

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

12. What does $Q_1$ represent in a box plot?

    The median of the lower half of the ordered data. First quartile marks the 25th percentile.

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

    All bins have equal width on the number line. Ensures fair comparison between intervals.

14. Find the median for the data set $[2,5,8,9,12]$.

    $8$. Middle value of 5 ordered values is the 3rd one.

15. A box plot has $Q_1 = 10$ and $Q_3 = 18$. What percent of the data lie between $10$ and $18$?

    $50\%$. The box always contains the middle 50% of data.

16. What is a histogram used to display on a number line?

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

17. What is a dot plot used to display on a number line?

    Data values with dots; each dot represents $1$ occurrence. Shows individual data points clearly on a number line.

18. What does each dot represent in a dot plot when no stacking is needed?

    One data value (one observation). Each dot marks one occurrence of that specific value.

19. Which plot groups data into equal-width intervals (bins) on a number line: dot plot, histogram, or box plot?

    Histogram. Groups data into bins with bars showing frequency.

20. Identify the part of a box plot that shows the middle $50\%$ of the data.

    The box from $Q_1$ to $Q_3$. The box contains the middle two quartiles.

21. Identify what the height of a bar in a histogram represents.

    The frequency (count) of data in that interval. Bar height shows how many values fall in that bin.

22. Identify $Q_1$ for the sorted data $\{1,2,4,7,9,10,11,12\}$ using the median-of-halves method.

    $3$. Median of lower half $\{1,2,4,7\}$ is $(2+4)/2$.

23. Find the IQR if $Q_1 = 6$ and $Q_3 = 14$.

    $8$. Subtract: $14 - 6 = 8$.

24. What is the interquartile range (IQR) in a box plot written as a formula?

    $\text{IQR} = Q_3 - Q_1$. Measures the spread of the middle 50% of data.

25. What is a dot plot on a number line used to display?

    A data set by marking a dot above each value on a number line. Shows distribution by placing dots at their values on the number line.

26. Find $IQR$ if $Q_1 = 6$ and $Q_3 = 14$.

    $14 - 6 = 8$. Subtract first quartile from third quartile.

27. Find the frequency of $3$ in this data set: $[1,3,3,3,4,5]$.

    $3$. Count occurrences: the value $3$ appears three times.

28. Which plot is best to show how many values fall in intervals for a large data set?

    Histogram. Histograms efficiently group and display large data sets.

29. Which plot is best for showing exact repeated values: dot plot, histogram, or box plot?

    Dot plot. Each dot shows one occurrence, perfect for duplicates.

30. What does the median represent in a data set?

    The middle value when the data are ordered. Splits ordered data into two equal halves.

31. Find the median of the ordered data set $2, 4, 7, 9, 10$.

    $7$. Middle value of odd-sized set is the 3rd of 5 values.

32. In a box plot, what do the whiskers represent?

    The minimum and maximum values (ends of the data). Whiskers extend to show the full range of the data.

33. What do the whiskers of a box plot represent in a standard grade-level box plot?

    They extend from $Q_1$ to minimum and from $Q_3$ to maximum. Show the spread from quartiles to extremes.

34. Find the range for the data set $[4,7,7,10]$.

    $6$. Range = maximum - minimum = $10 - 4 = 6$.

35. What is a box plot (box-and-whisker plot) used to display?

    A distribution using the five-number summary. Shows spread and center using quartiles visually.

36. A histogram bin labeled $10\text{–}15$ has height $7$. How many data values are in $10\text{–}15$?

    $7$ values. Height equals count of values in that interval.

37. A dot plot shows $3$ dots at $4$ and $2$ dots at $6$. How many data values are shown total?

    $5$. Count all dots: $3 + 2 = 5$.

38. What are the five numbers in the five-number summary for a box plot?

    Minimum, $Q_1$, median, $Q_3$, maximum. These values divide data into four equal parts.

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

    The frequency (count) in that interval. Bar height shows how many data points fall in that bin.

40. What does $Q_3$ represent in a box plot?

    The median of the upper half of the ordered data. Third quartile marks the 75th percentile.

41. What is a dot plot on a number line used to show about a data set?

    A dot above each value shows its frequency on a number line. Each dot represents one data value's position on the number line.

42. Which plot is best for large data sets grouped into intervals: dot plot, histogram, or box plot?

    Histogram. Bins organize many values into manageable groups.

43. Which plot is best for quickly comparing spread using quartiles: dot plot, histogram, or box plot?

    Box plot. Shows five-number summary at a glance.

44. Identify the median of the data set $\{1,4,6,8\}$.

    $5$. Average of middle two: $(4+6)/2 = 5$.

45. A histogram bin $[20,30)$ has bar height $6$. What does $6$ mean in this context?

    $6$ data values are in $[20,30)$. Bar height shows count of values in that bin.

46. What are the five numbers in the five-number summary for a box plot?

    Minimum, $Q_1$, median, $Q_3$, maximum. These divide the data into quarters.

47. Identify the plot type that groups data into equal-width intervals (bins) on a number line.

    Histogram. Groups continuous data into bins with bars showing frequencies.

48. In a box plot, what does the vertical line inside the box represent?

    The median. Shows the middle value that splits data in half.

49. What is a box plot (box-and-whisker plot) used to display from a data set?

    The five-number summary on a number line. Shows min, $Q_1$, median, $Q_3$, and max values.

50. What is the range formula for a data set?

    $\text{range} = \text{maximum} - \text{minimum}$. Measures total spread from smallest to largest value.

51. What is the meaning of a stack of $4$ dots above the value $7$ in a dot plot?

    The value $7$ occurs $4$ times. Each dot represents one occurrence of that value.

52. Identify the median of the data set $\{2,3,3,5,9\}$.

    $3$. Middle value when ordered: $2, 3, 3, 5, 9$.

53. In a histogram with bins $[0,5)$, $[5,10)$, $[10,15)$, which bin contains the value $10$?

    $[10,15)$. Square bracket includes the endpoint.

54. Find the median of the ordered data set $3, 5, 8, 12$.

    $\frac{5+8}{2} = 6.5$. For even-sized sets, average the two middle values.

55. What is the interquartile range, written as a formula?

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

56. Find $Q_3$ for the data set $[1,2,4,6,9,10,12,15]$.

    $11$. $Q_3$ is median of upper half: median of $[9,10,12,15]$ is $11$.

57. Find the range of the data set with minimum $4$ and maximum $19$.

    $19 - 4 = 15$. Subtract minimum from maximum for total spread.

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