7. a circle graph is being drawn to track school elective choices. if $40\%$ of the student body chose \art\, how many degrees out of a full $360^\circ$ circle must the central angle for the art sector be?

8. a bar graph uses a scale where $1\text{ cm}$ of bar height represents $5$ books read. if the bar for sarahs reading log is $6.5\text{ cm}$ high, how many books did she read?

9. a double-line graph tracks the speed of two runners. at the 10-minute mark, runner a is traveling at $12\text{ km/h}$ and runner b is at $9\text{ km/h}$. express the ratio of runner bs speed to runner as speed as a fraction in simplest form.

10. you have a set of five test scores: $70, 75, 80, 85,$ and $90$. if you add a sixth score of $80$ to this data set, will the median increase, decrease, or stay the exact same?

11. a continuous histogram groups student travel times to school. one interval bar labeled \10 to 20 minutes\ has a frequency height of $14$ students. can we use this graph to find out exactly how many students take exactly $15$ minutes to get to school? (answer yes or no, and provide a 1-sentence reason).

12. a store owner wants to show the steady upward trend of their sales month-by-month over a 12-month period. which type of visual representation is better for highlighting this continuous change over time: a line graph or a bar graph?

13. the mean of four numbers is exactly $15$. if three of the numbers are $10, 12,$ and $18$, what must the fourth number be?

14. a data set contains the following values: $3, 5, 8, 12, 17, 21$. what is the median of this data set?

Question

7. a circle graph is being drawn to track school elective choices. if $40\%$ of the student body chose \art\, how many degrees out of a full $360^\circ$ circle must the central angle for the art sector be?

8. a bar graph uses a scale where $1\text{ cm}$ of bar height represents $5$ books read. if the bar for sarahs reading log is $6.5\text{ cm}$ high, how many books did she read?

9. a double-line graph tracks the speed of two runners. at the 10-minute mark, runner a is traveling at $12\text{ km/h}$ and runner b is at $9\text{ km/h}$. express the ratio of runner bs speed to runner as speed as a fraction in simplest form.

10. you have a set of five test scores: $70, 75, 80, 85,$ and $90$. if you add a sixth score of $80$ to this data set, will the median increase, decrease, or stay the exact same?

11. a continuous histogram groups student travel times to school. one interval bar labeled \10 to 20 minutes\ has a frequency height of $14$ students. can we use this graph to find out exactly how many students take exactly $15$ minutes to get to school? (answer yes or no, and provide a 1-sentence reason).

12. a store owner wants to show the steady upward trend of their sales month-by-month over a 12-month period. which type of visual representation is better for highlighting this continuous change over time: a line graph or a bar graph?

13. the mean of four numbers is exactly $15$. if three of the numbers are $10, 12,$ and $18$, what must the fourth number be?

14. a data set contains the following values: $3, 5, 8, 12, 17, 21$. what is the median of this data set?

Accepted Answer

{ "quality": "clear", "question_count": 8, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Data Interpretation", "Basic Statistics", "Graph Selection" ], "current_concepts": [ "Data Interpretation", "Basic Statistics", "Graph Selection" ] } ## Question 7: Calculate central angle for Art sector $$ 360^\circ \times 0.40 = 144^\circ $$ ## Question 8: Calculate total books read $$ 6.5 \text{ cm} \times 5 \text{ books/cm} = 32.5 \text{ books} $$ ## Question 9: Express ratio of Runner B to Runner A $$ \frac{\text{Runner B}}{\text{Runner A}} = \frac{9}{12} = \frac{3}{4} $$ ## Question 10: Determine median change $$ \begin{aligned} &\text{Original set: } \{70, 75, 80, 85, 90\} \implies \text{Median} = 80\ &\text{New set: } \{70, 75, 80, 80, 85, 90\} \implies \text{Median} = \frac{80 + 80}{2} = 80 \end{aligned} $$ ## Question 11: Analyze histogram interval data $$ \text{No. Histograms show interval frequencies, not individual data values.} $$ ## Question 12: Select graph type for continuous change $$ \text{Line graph} $$ ## Question 13: Solve for the fourth number $$ \begin{aligned} &10 + 12 + 18 + x = 15 \times 4\ &40 + x = 60\ &x = 20 \end{aligned} $$ ## Question 14: Find the median of the data set $$ \begin{aligned} &\text{Sorted set: } \{3, 5, 8, 12, 17, 21\}\ &\text{Median} = \frac{8 + 12}{2} = 10 \end{aligned} $$ ## Question 7 $144^\circ$ ## Question 8 $32.5$ books ## Question 9 $\frac{3}{4}$ ## Question 10 Stay the exact same ## Question 11 No, because a histogram only shows the total number of data points within an interval, not the specific individual values. ## Question 12 A line graph ## Question 13 $20$ ## Question 14 $10$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Statistics", "Data Interpretation" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 7: Calculate central angle for Art sector

Question 8: Calculate total books read

Question 9: Express ratio of Runner B to Runner A

Question 10: Determine median change

Question 11: Analyze histogram interval data

Question 12: Select graph type for continuous change

Question 13: Solve for the fourth number

Question 14: Find the median of the data set

Answer:

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14