(a) find the five-number summary, and (b) draw a box-and-whisker plot of the data.

4 8 8 6 2 9 8 7 9 6 9 4 1 6 2 9 8 7 7 9

(a) $\text{min} = 1$ (simplify your answer.)

$q_1 = 5$ (simplify your answer.)

$q_2 = 7$ (simplify your answer.)

$q_3 = \square$ (simplify your answer.)

Question

(a) find the five-number summary, and (b) draw a box-and-whisker plot of the data.

4 8 8 6 2 9 8 7 9 6 9 4 1 6 2 9 8 7 7 9

(a) $\text{min} = 1$ (simplify your answer.)

$q_1 = 5$ (simplify your answer.)

$q_2 = 7$ (simplify your answer.)

$q_3 = \square$ (simplify your answer.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Five-Number Summary" ], "new_concepts": [], "current_concepts": [ "Five-Number Summary", "Box-and-Whisker Plot" ] } ## Sort the dataset Using the *Five-Number Summary* knowledge point $$ \text{Original: } 4, 8, 8, 6, 2, 9, 8, 7, 9, 6, 9, 4, 1, 6, 2, 9, 8, 7, 7, 9 $$ $$ \text{Sorted: } 1, 2, 2, 4, 4, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9 $$ $$ N = 20 $$ ## Find the median and quartiles Using the *Five-Number Summary* knowledge point $$ \begin{aligned} &\text{Min} = 1\ &\text{Max} = 9\ &Q_2 = \frac{\text{Value}_{10} + \text{Value}_{11}}{2} = \frac{7 + 7}{2} = 7\ &\text{Lower Half (first 10 values): } 1, 2, 2, 4, 4, 6, 6, 6, 7, 7\ &Q_1 = \frac{\text{Value}_5 + \text{Value}_6}{2} = \frac{4 + 6}{2} = 5\ &\text{Upper Half (last 10 values): } 7, 8, 8, 8, 8, 9, 9, 9, 9, 9\ &Q_3 = \frac{\text{Value}_{15} + \text{Value}_{16}}{2} = \frac{8 + 9}{2} = 8.5 \end{aligned} $$ $Q_3 =$ $8.5$ { "elements": [ { "type": "line", "params": [[1, 0], [9, 0]], "properties": { "strokeColor": "#583C87", "strokeWidth": 1, "dash": 1 } }, { "type": "segment", "params": [[1, 0], [5, 0]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "segment", "params": [[8.5, 0], [9, 0]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "polygon", "params": [[5, -1], [8.5, -1], [8.5, 1], [5, 1]], "properties": { "fillColor": "rgba(140, 85, 242, 0.15)", "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "segment", "params": [[7, -1], [7, 1]], "properties": { "strokeColor": "#F2557F", "strokeWidth": 3 } }, { "type": "segment", "params": [[1, -0.5], [1, 0.5]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "segment", "params": [[9, -0.5], [9, 0.5]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "point", "params": [[1, 0]], "properties": { "name": "Min=1", "withLabel": true, "color": "#8C55F2", "size": 3 } }, { "type": "point", "params": [[5, 0]], "properties": { "name": "Q1=5", "withLabel": true, "color": "#8C55F2", "size": 3 } }, { "type": "point", "params": [[7, 0]], "properties": { "name": "Q2=7", "withLabel": true, "color": "#F2557F", "size": 3 } }, { "type": "point", "params": [[8.5, 0]], "properties": { "name": "Q3=8.5", "withLabel": true, "color": "#8C55F2", "size": 3 } }, { "type": "point", "params": [[9, 0]], "properties": { "name": "Max=9", "withLabel": true, "color": "#8C55F2", "size": 3 } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Five-Number Summary" ] }

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QUESTION IMAGE

Question

Explanation:

Sort the dataset

Find the median and quartiles

Answer: