Question

line plots
weight of each bag of candy (in pounds)
key
x = weight of 1 piece of candy

1. how many bags weigh less than $\frac{1}{2}$ of a pound?
2. how many bags weigh at least $\frac{3}{4}$ of a pound?
3. how many bags of candy were weighed?
4. how many bags weigh more than $\frac{3}{4}$ of a pound?
5. what is the combined weight of the four heaviest bags of candy?
6. if you combined the candy and redistributed it evenly among the 9 bags, how much candy would be in each bag? (mean)

Explanation:

Step1: Count bags less than $\frac{1}{2}$ pound

There is 1 bag at $\frac{1}{4}$ pound. So, the number of bags weighing less than $\frac{1}{2}$ pound is 1.

Step2: Count bags at least $\frac{3}{4}$ pound

There are 2 bags at $\frac{3}{4}$ pound, 3 bags at 1 pound and 1 bag at $1\frac{1}{4}$ pound. So, $2 + 3+1=6$ bags weigh at least $\frac{3}{4}$ pound.

Step3: Count total bags

Count all the 'X's. There are $1 + 2+2 + 3+1=9$ bags of candy weighed.

Step4: Count bags more than $\frac{3}{4}$ pound

There are 3 bags at 1 pound and 1 bag at $1\frac{1}{4}$ pound. So, $3 + 1=4$ bags weigh more than $\frac{3}{4}$ pound.

Step5: Calculate combined weight of four heaviest bags

The four heaviest bags are 3 bags at 1 pound and 1 bag at $1\frac{1}{4}$ pound. The combined weight is $3\times1+1\times1\frac{1}{4}=3 + 1\frac{1}{4}=4\frac{1}{4}$ pounds.

Step6: Calculate mean weight

The total weight of all 9 bags is $1\times\frac{1}{4}+2\times\frac{1}{2}+2\times\frac{3}{4}+3\times1 + 1\times1\frac{1}{4}=\frac{1}{4}+1+\frac{3}{2}+3+\frac{5}{4}=\frac{1 + 4+6 + 12+5}{4}=\frac{28}{4} = 7$ pounds. The mean weight is $\frac{7}{9}$ pounds.

Answer:

1. 1
2. 6
3. 9
4. 4
5. $4\frac{1}{4}$ pounds
6. $\frac{7}{9}$ pounds