3. calculate the 5 number summary. round to the nearest tenth if needed. construct a box-and-whisker plot.

data set: 59 77 69 61 73 82 67 66 55 89 67 86

Question

3. calculate the 5 number summary. round to the nearest tenth if needed. construct a box-and-whisker plot.

data set: 59 77 69 61 73 82 67 66 55 89 67 86

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Five-Number Summary", "Box-and-Whisker Plot" ], "current_concepts": [ "Five-Number Summary", "Box-and-Whisker Plot", "Percentiles and Quartiles" ] } ## Order the data set $$ 55, 59, 61, 66, 67, 67, 69, 73, 77, 82, 86, 89 $$ ## Calculate the five-number summary $$ \begin{aligned} &n = 12\ &\text{Minimum} = 55\ &\text{Maximum} = 89\ &\text{Median } (Q_2) = \frac{67 + 69}{2} = 68\ &\text{Lower Half: } 55, 59, 61, 66, 67, 67 \implies Q_1 = \frac{61 + 66}{2} = 63.5\ &\text{Upper Half: } 69, 73, 77, 82, 86, 89 \implies Q_3 = \frac{77 + 82}{2} = 79.5 \end{aligned} $$ ## Verify the summary values $$ \begin{aligned} &\text{Min} = 55\ &Q_1 = 63.5\ &\text{Median} = 68\ &Q_3 = 79.5\ &\text{Max} = 89 \end{aligned} $$ The five-number summary for the data set is: - **Minimum:** 55 - **First Quartile ($Q_1$):** 63.5 - **Median ($Q_2$):** 68 - **Third Quartile ($Q_3$):** 79.5 - **Maximum:** 89 { "elements": [ { "type": "line", "params": [[50, 0], [95, 0]], "properties": { "strokeColor": "#583C87", "strokeWidth": 1, "fixed": true } }, { "type": "segment", "params": [[55, 0], [63.5, 0]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "dash": 2 } }, { "type": "segment", "params": [[79.5, 0], [89, 0]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "dash": 2 } }, { "type": "segment", "params": [[55, -0.5], [55, 0.5]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "segment", "params": [[89, -0.5], [89, 0.5]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "polygon", "params": [[63.5, -1], [79.5, -1], [79.5, 1], [63.5, 1]], "properties": { "fillColor": "rgba(140, 85, 242, 0.15)", "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "segment", "params": [[68, -1], [68, 1]], "properties": { "strokeColor": "#F2557F", "strokeWidth": 3 } }, { "type": "point", "params": [[55, 0]], "properties": { "name": "Min: 55", "size": 3, "color": "#8C55F2", "withLabel": true, "labelPosition": [55, -1.5] } }, { "type": "point", "params": [[63.5, 0]], "properties": { "name": "Q1: 63.5", "size": 3, "color": "#8C55F2", "withLabel": true, "labelPosition": [63.5, 1.8] } }, { "type": "point", "params": [[68, 0]], "properties": { "name": "Med: 68", "size": 3, "color": "#F2557F", "withLabel": true, "labelPosition": [68, -1.8] } }, { "type": "point", "params": [[79.5, 0]], "properties": { "name": "Q3: 79.5", "size": 3, "color": "#8C55F2", "withLabel": true, "labelPosition": [79.5, 1.8] } }, { "type": "point", "params": [[89, 0]], "properties": { "name": "Max: 89", "size": 3, "color": "#8C55F2", "withLabel": true, "labelPosition": [89, -1.5] } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Statistics", "Five-Number Summary" ] }

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Question

Explanation:

Order the data set

Calculate the five-number summary

Verify the summary values

Answer: