The dot plots show the number of hours a group of fifth graders and seventh graders spent playing outdoors over a one-week period.
Time Spent Playing Outdoors
for Fifth Graders and Seventh Graders
2 dot plots with number lines going from 0 to 10. A dot plot titled fifth grade has 0 dots above 0, 2 above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, and 0 and 9 and 10. A dot plot titled seventh grade has 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.
Which statement correctly compares the shape of the data in the plots?
o Both sets of data have a peak at 5 hours and 6 hours.
o In the seventh-grade data, the left side of the data looks similar to the right side, but not in the fifth-grade data.
o In both sets, the data cluster around 3 hours.
o There is a gap in the seventh-grade data, but not in the fifth-grade data.
To compare the shape of the data in the dot plots, we need to analyze the distribution of the dots. Here's how you can determine the correct statement:
1. Count the number of dots at each value on the number line for both the fifth-grade and seventh-grade dot plots.
- For the fifth-grade dot plot, count the number of dots at each value from 0 to 10.
- For the seventh-grade dot plot, count the number of dots at each value from 0 to 10.
2. Look for patterns in the distribution of the dots in each dot plot.
Let's follow these steps:
1. Counting the dots in the fifth-grade dot plot:
- 0 hours: 0 dots
- 1 hour: 2 dots
- 2 hours: 3 dots
- 3 hours: 1 dot
- 4 hours: 4 dots
- 5 hours: 5 dots
- 6 hours: 5 dots
- 7 hours: 2 dots
- 8 hours: 2 dots
- 9 hours: 0 dots
- 10 hours: 0 dots
2. Counting the dots in the seventh-grade dot plot:
- 0 hours: 2 dots
- 1 hour: 2 dots
- 2 hours: 3 dots
- 3 hours: 5 dots
- 4 hours: 5 dots
- 5 hours: 3 dots
- 6 hours: 3 dots
- 7 hours: 1 dot
- 8 hours: 0 dots
- 9 hours: 0 dots
- 10 hours: 0 dots
Now, let's analyze the patterns:
- Option 1: "Both sets of data have a peak at 5 hours and 6 hours."
- Looking at the dot plots, we can see that this statement is incorrect. Although both sets have a peak around 5 hours, the seventh-grade dot plot does not have a peak around 6 hours, suggesting that the data sets do not have the same shape.
- Option 2: "In the seventh-grade data, the left side of the data looks similar to the right side, but not in the fifth-grade data."
- By comparing the dot plots, we can observe that the seventh-grade dot plot does have a similar distribution on both sides, while the fifth-grade dot plot does not. Therefore, this statement is correct.
- Option 3: "In both sets, the data cluster around 3 hours."
- Analyzing the dot plots, we can see that neither set has a significant cluster around 3 hours. So, this statement is incorrect.
- Option 4: "There is a gap in the seventh-grade data, but not in the fifth-grade data."
- Looking at the seventh-grade dot plot, we can see a gap around 8, 9, and 10 hours, while the fifth-grade dot plot doesn't have a gap. Therefore, this statement is correct.
Based on the analysis, the correct statement that compares the shape of the data in the plots is: "In the seventh-grade data, the left side of the data looks similar to the right side, but not in the fifth-grade data."