dot plot detective\ncase 1: hours spent studying\nbelow is a dot - plot showing the number of hours 13…
dot plot detective\ncase 1: hours spent studying\nbelow is a dot - plot showing the number of hours 13 students studied for a math test.\nquestions:\n1. how many students studied 4 hours?\n2. what is the most common number of hours studied?\n3. how many total students are represented?\n4. what is the range of hours studied?\n5. what percentage of students studied 3 or more hours?\ncase 2: favorite ice cream flavors\na class of students voted on their favorite ice cream flavor. the dot - plot shows the results.\nchocolate ● ● ● ● ●\nvanilla ● ● ●\nmint ● ● ● ●\nstrawberry ● ●\ncookies & cream ●\nquestions:\n6. which flavor is the most popular?\n7. how many students voted for vanilla or mint?\n8. which flavor received the least votes?\n9. what is the total number of votes?\n10. what fraction of the class voted for chocolate?\ncase 3: be the analyst\ndot plot: number of books read in a month\nquestions:\n11. how many students read fewer than 2 books?\n12. what is the median number of books read?\n13. if the student who read 4 books read 2 more books next month, how would that affect the dot - plot?\n14. which is greater: the mean or the median? explain why.
Answer
Explanation:
Step1: Analyze Case 1 dot - plot
Count dots for each value.
Step2: Answer Case 1 questions
- Count dots above 3 hours: 5 students studied 3 or more hours.
- The most common number is the value with most dots. Here, 2 hours (4 dots).
- Total number of students is sum of all dots, 12.
- Range = Maximum - Minimum. Maximum is 5, minimum is 1, so range is 5 - 1=4.
- Number of students who studied 3 or more hours is 5. Percentage = $\frac{5}{12}\times100%\approx41.67%$.
Step3: Analyze Case 2 dot - plot
Count dots for each flavor.
Step4: Answer Case 2 questions
- Chocolate has most dots, so it is the most popular.
- Vanilla has 3 dots, Mint has 4 dots. Total = 3 + 4=7 students voted for Vanilla or Mint.
- Strawberry has fewest votes (2 dots).
- Total number of votes = 5 (Chocolate)+3 (Vanilla)+4 (Mint)+2 (Strawberry)+1 (Cookies & Cream)=15.
- Fraction for Chocolate = $\frac{5}{15}=\frac{1}{3}$.
Step5: Analyze Case 3 dot - plot
Count dots for each number of books.
Step6: Answer Case 3 questions
- Number of students who read fewer than 2 books: Dots for 0 and 1 book. 2 (0 - book students)+3 (1 - book students)=5 students.
- First, order data set. There are 12 data - points. Median is average of 6th and 7th ordered values. Ordered data: 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4. Median = $\frac{1 + 2}{2}=1.5$.
- If student who read 4 books read 2 books instead, the dot above 4 would move to above 2. This would decrease the mean (as sum of values decreases) and may or may not change median depending on new ordering (but in this case, median would remain 1.5).
- Mean = $\frac{0\times2 + 1\times3+2\times3 + 3\times2+4\times1}{12}=\frac{0 + 3+6 + 6+4}{12}=\frac{19}{12}\approx1.58$. Median = 1.5. Mean is greater because the larger values (3 and 4) pull the mean up.
Answer:
- 5 students
- 2 hours
- 12 students
- 4 hours
- Approximately 41.67%
- Chocolate
- 7 students
- Strawberry
- 15 votes
- $\frac{1}{3}$
- 5 students
- 1.5 books
- The dot above 4 would move to above 2, mean would decrease, median may remain the same (in this case it does).
- The mean is greater. Mean $\approx1.58$, median = 1.5. Larger values (3 and 4) pull the mean up.