Question

In the previous lesson, you learned that statistical data varies. In this lesson, you’ll

learn to explain variability in data. Take a look at this problem.

Students in band, chorus, and strings classes collected donations for a fundraiser

concert to raise money for the music program. These line plots show the results of

asking 10 students from each class how much money they collected.

Money Raised ($)

Band

X

X

X

X

X

X

X

X X X

0 10 20 30 40 50 60

Money Raised ($)

Chorus

X

X

X

X

X

X

X

X

X

X

0 10 20 30 40 50 60

Money Raised ($)

Strings

X

X

X

X

X

X

X

X

X X

0 10 20 30 40 50 60

Use the shape of each line plot to explain how the data vary.

Use the math you already know to solve this problem.

a. Between what numbers are the most common responses for each group of students?

Band Chorus

Strings

b. Based on the line plots, which class likely raised the most money? Explain.

c. Based on the line plots, which class likely raised the least money? Explain.

d. Do you think these graphs would look different if 10 different students were surveyed

from each class? Explain.

Answer 1

To analyze the data from the line plots of money raised by students in band, chorus, and strings classes, let’s break down the answers to the questions:

### a. Between what numbers are the most common responses for each group of students?
The most common responses for each group can be determined by identifying where the X's are most concentrated in each line plot.

- **Band:** The highest concentration of X's is between **$10 to $30**. Most students raised around these amounts.
- **Chorus:** The highest concentration of X's is between **$10 to $20**. This indicates that many students collected amounts in this range.
- **Strings:** The highest concentration of X's is between **$20 to $40**. This means many students raised money in this interval.

### b. Based on the line plots, which class likely raised the most money? Explain.
The class that likely raised the most money is the **Strings** class. This conclusion is based on the fact that there were more X's clustered around the higher amounts ($20 to $60), suggesting a greater overall amount collected compared to the other classes.

### c. Based on the line plots, which class likely raised the least money? Explain.
The class that likely raised the least money is the **Chorus** class. The concentration of X's is lower overall, especially around the higher amounts, indicating that more students likely raised less money compared to those in the Band and Strings.

### d. Do you think these graphs would look different if 10 different students were surveyed from each class? Explain.
Yes, these graphs could look different if 10 different students were surveyed from each class. Variability in individual student contributions can lead to differences in the data collected. For example, if a different group of students participated, it’s possible they could collectively have higher or lower donations, or the distribution of the amounts raised could have changed significantly, reflecting different fundraising efforts or financial circumstances among different groups of students.

In summary, through visual analysis of the line plots, we can determine common money raised ranges, which class likely raised the most or least money, and that variability in the groups could lead to different results if surveyed again.