Question

the dot plot shows the amount of milk, in gallons, that seventeen students drank during the first week of school. how many students drank more than one - half of a gallon of milk?
a 13
b 11

Explanation:

Step1: Determine half - gallon in sixths

One - half of a gallon is $\frac{1}{2}$ gallon. To convert this to sixths, we know that $\frac{1}{2}=\frac{3}{6}$ (since $6\div2 = 3$). So we need to find the number of students who drank more than $\frac{3}{6}$ gallon.

Step2: Identify the categories above $\frac{3}{6}$

The values on the dot - plot are $\frac{1}{6},\frac{2}{6},\frac{3}{6},\frac{4}{6},\frac{5}{6},\frac{6}{6}$. We need to consider the values $\frac{4}{6},\frac{5}{6},\frac{6}{6}$.

• For $\frac{4}{6}$: Count the number of dots. There are 4 dots.
• For $\frac{5}{6}$: Count the number of dots. There are 6 dots.
• For $\frac{6}{6}$: Count the number of dots. There is 1 dot.

Step3: Sum the number of dots

Now we sum the number of dots for $\frac{4}{6},\frac{5}{6},\frac{6}{6}$. So $4 + 6+1=11$? Wait, no, wait. Wait, let's re - check. Wait, $\frac{3}{6}$ is the boundary. More than $\frac{3}{6}$ means $\frac{4}{6},\frac{5}{6},\frac{6}{6}$. Wait, $\frac{4}{6}$ has 4 dots, $\frac{5}{6}$ has 6 dots, $\frac{6}{6}$ has 1 dot? Wait, no, looking at the dot - plot:

• $\frac{1}{6}$: 1 dot
• $\frac{2}{6}$: 3 dots
• $\frac{3}{6}$: 2 dots
• $\frac{4}{6}$: 4 dots
• $\frac{5}{6}$: 6 dots
• $\frac{6}{6}$: 1 dot

Wait, we need students who drank more than $\frac{1}{2}=\frac{3}{6}$ gallon. So we exclude $\frac{1}{6},\frac{2}{6},\frac{3}{6}$. The number of students with $\frac{1}{6}$: 1, $\frac{2}{6}$: 3, $\frac{3}{6}$: 2. Total students: $1 + 3+2 + 4+6 + 1=17$ (which matches the problem statement). So the number of students who drank more than $\frac{3}{6}$ is total students minus students with $\frac{1}{6},\frac{2}{6},\frac{3}{6}$. So $17-(1 + 3+2)=17 - 6 = 11$? Wait, no, $1+3 + 2=6$, $17-6 = 11$? Wait, but wait, $\frac{4}{6}$ is 4, $\frac{5}{6}$ is 6, $\frac{6}{6}$ is 1. $4 + 6+1=11$. Yes, that's correct.

Wait, but let's check again. The question is "how many students drank more than one - half of a gallon". One - half is $\frac{3}{6}$. So more than $\frac{3}{6}$ is $\frac{4}{6},\frac{5}{6},\frac{6}{6}$. So:

• $\frac{4}{6}$: 4 students
• $\frac{5}{6}$: 6 students
• $\frac{6}{6}$: 1 student

Sum: $4 + 6+1 = 11$? Wait, no, $4+6 = 10$, $10 + 1=11$. Wait, but the option B is 11. Wait, but let's check the dot - plot again. Wait, maybe I miscounted. Wait, the $\frac{5}{6}$ has 6 dots? Let's see the original dot - plot:

Looking at the vertical stacks:

• First stack ($\frac{1}{6}$): 1 dot
• Second stack ($\frac{2}{6}$): 3 dots (three dots)
• Third stack ($\frac{3}{6}$): 2 dots (two dots)
• Fourth stack ($\frac{4}{6}$): 4 dots (four dots)
• Fifth stack ($\frac{5}{6}$): 6 dots (six dots)
• Sixth stack ($\frac{6}{6}$): 1 dot (one dot)

Total students: $1+3 + 2+4 + 6+1=17$, which matches. Now, students who drank more than $\frac{3}{6}$ (i.e., $\frac{4}{6},\frac{5}{6},\frac{6}{6}$) are $4 + 6+1 = 11$. So the number of students is 11.

Answer:

B. 11