Questions: (a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 38842987959326298779 (a) Min=2 (Simplify your answer.) Q1= (Simplify your answer. Do not round.)

(a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 38842987959326298779 (a) Min=2 (Simplify your answer.) Q1= (Simplify your answer. Do not round.)
Transcript text: (a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. \[ 38842987959326298779 \] (a) $\operatorname{Min}=2$ (Simplify your answer.) $Q_{1}=$ $\square$ (Simplify your answer. Do not round.)
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Solution

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Solution Steps

Step 1: Find the Five-Number Summary

The five-number summary consists of the minimum, first quartile ($Q_1$), median, third quartile ($Q_3$), and maximum of a data set. Given the data set:

\[ 3, 8, 8, 4, 2, 9, 8, 7, 9, 5, 9, 3, 2, 6, 5, 4, 7, 8, 9, 7, 9 \]

  1. Minimum: The smallest number in the data set is 2.
  2. Maximum: The largest number in the data set is 9.
  3. Median: Arrange the data in ascending order and find the middle value.
    • Ordered data: 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9
    • Median: The middle value is 7.
  4. First Quartile ($Q_1$): The median of the first half of the data.
    • First half: 2, 2, 3, 3, 4, 4, 5, 5, 6
    • $Q_1$: The median of this set is 4.
  5. Third Quartile ($Q_3$): The median of the second half of the data.
    • Second half: 7, 8, 8, 8, 8, 9, 9, 9, 9, 9
    • $Q_3$: The median of this set is 9.

Final Answer

The five-number summary is:

  • Minimum: 2
  • $Q_1$: 4
  • Median: 7
  • $Q_3$: 9
  • Maximum: 9

{"axisType": 3, "coordSystem": {"xmin": 0, "xmax": 10, "ymin": 0, "ymax": 10}, "commands": ["y = 2", "y = 4", "y = 7", "y = 9", "y = 9"], "latex_expressions": ["$Min = 2$", "$Q_1 = 4$", "$Median = 7$", "$Q_3 = 9$", "$Max = 9$"]}

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