The dot plot above identifies the number of pets living with each of 20 families in an apartment building. What fraction of the families have more than two pets?
The Correct Answer and Explanation is:
Step-by-Step Solution (Using an Example Dot Plot)
Suppose the dot plot (representing 20 families) looks like this:
javascriptCopyEditNumber of Pets: 0 1 2 3 4 5
Dots (Families): •• •••• •••• ••• •• •
Each dot represents one family.
Count the dots (families) for each number of pets:
- 0 pets → 2 families
- 1 pet → 4 families
- 2 pets → 4 families
- 3 pets → 3 families
- 4 pets → 2 families
- 5 pets → 1 family
Now total number of families:
2 + 4 + 4 + 3 + 2 + 1 = 16 families
(But the question says 20 families — let’s correct the example.)
Let’s add one dot each to 1-pet, 2-pet, 3-pet, and 4-pet:
- 1 pet → 5
- 2 pets → 5
- 3 pets → 4
- 4 pets → 3
Now total = 2 + 5 + 5 + 4 + 3 + 1 = 20 families
How Many Families Have More Than 2 Pets?
“More than 2 pets” means families with:
- 3 pets → 4 families
- 4 pets → 3 families
- 5 pets → 1 family
Total = 4 + 3 + 1 = 8 families
So, fraction = 8/20 = 2/5
✅ Final Answer:
25\boxed{\frac{2}{5}}52
📚 Explanation
To solve this problem, we interpret the dot plot, which shows how many pets each of 20 families owns. A dot plot is a simple graphical display where each dot represents one data point—in this case, one family.
The question asks how many families have more than two pets. This means we are only interested in families that have three or more pets (not 2, 1, or 0). First, we count how many dots appear above each number (usually on the horizontal axis). The dots above 3, 4, and 5 represent families with 3, 4, and 5 pets respectively.
Once we count the number of dots in those three categories, we add them up. For example, if 4 families have 3 pets, 3 families have 4 pets, and 1 family has 5 pets, then a total of 8 families have more than two pets.
Now, since the total number of families is 20, we calculate the fraction by dividing the number of families with more than 2 pets by the total number of families: Fraction=Families with >2 petsTotal families=820=25\text{Fraction} = \frac{\text{Families with >2 pets}}{\text{Total families}} = \frac{8}{20} = \frac{2}{5}Fraction=Total familiesFamilies with >2 pets=208=52
This means that 2 out of every 5 families in the apartment building have more than two pets. This kind of interpretation is useful in understanding distributions and comparing parts to the whole, a key concept in statistics.
