Question

For an engineering project, each student in Mr. McDonald's science class made a catapult and measured how far it flung a marshmallow. This box plot shows the results.
Marshmallow distance (in.)
0
20
40
60
80
100
What fraction of the catapults flung a marshmallow 30 inches or less?

Answer 1

To determine what fraction of the catapults flung a marshmallow 30 inches or less, you need to analyze the box plot based on the following key components:

1. **Minimum Value**: The smallest measurement in the data set.
2. **First Quartile (Q1)**: The value below which 25% of the data falls.
3. **Median (Q2)**: The middle value of the data set.
4. **Third Quartile (Q3)**: The value below which 75% of the data falls.
5. **Maximum Value**: The largest measurement in the data set.

From the box plot, observe the marking of the quartiles and other key points. You need to find how many values are at or below 30 inches.

- If the value of 30 inches is above the first quartile (Q1), this means fewer than 25% of the data falls below this value.
- If 30 inches is between Q1 and median, you’ll determine if more than 25% but less than half of the data falls below it.
- If 30 inches is lower than Q1, more than 75% of the data falls below it.

Assuming you visually analyzed the box plot and identified the quartiles:
- Count the number of students whose marshmallow distance is at or below 30 inches.
- Divide that number by the total number of students to find the fraction.

If you know the total number of students (say, for example, it is 20), and if you found that 5 of them flung marshmallows 30 inches or less, the fraction would be:

\[
\text{Fraction} = \frac{\text{Number of students throwing ≤30 inches}}{\text{Total number of students}} = \frac{5}{20} = \frac{1}{4}
\]

Please apply this logic to your data from the box plot you referenced to find the precise fraction.