There are 1,284
students at Latisha’s school. She surveys a representative sample of students about their monthly cell phone usage. The results are shown in the box plot.
The box plot is titled Monthly Cell Phone Usage. The number line is labeled Number of Minutes and goes from four hundred to one thousand by a scale of one hundred. The whiskers range from four hundred to one thousand minutes, and the box ranges from six hundred to eight hundred minutes. A line divides the box at seven hundred minutes.
Use the box plot to make inferences about the population from the sample data.
Enter the correct answers in the boxes.
%
use 800
or more minutes
%
use 600
to 800
minutes
students use 600
or fewer minutes
Since there are 1,284 students at the school and Latisha used a representative sample, we can estimate the percent of students in each category based on the box plot.
To estimate percentage for students using 800 or more minutes, we look at the higher whisker of the box plot which starts at 800 and ends at 1000 minutes. Since this whisker represents the upper 25% of the sample (the upper quartile), we can estimate that 25% of the students use 800 or more minutes.
For students using 600 to 800 minutes, we look at the box part of the box plot. The box starts at 600 and ends at 800 minutes. Half of the students will be in this range which is 50%.
Lastly, to determine the percent of students using 600 or fewer minutes, we analyze the lower whisker of the box plot which starts at 400 and ends at 600 minutes. Similar to the higher whisker, the lower whisker also represents the lower 25% of the sample data. So we can estimate that 25% of students use 600 or fewer minutes.
In summary,
- 25% of students use 800 or more minutes
- 50% of students use 600 to 800 minutes
- 25% of students use 600 or fewer minutes
To make inferences about the population from the sample data, we can use the information provided in the box plot.
- % use 800 or more minutes:
Looking at the box plot, we can see that the upper whisker extends up to one thousand minutes. We also know that the box ranges from six hundred to eight hundred minutes, with a line dividing it at seven hundred minutes. From this information, we can infer that the percentage of students who use 800 or more minutes would be 0% since there is no data point above 800 minutes in the box plot.
- % use 600 to 800 minutes:
From the box plot, we can see that the box ranges from six hundred to eight hundred minutes. The line dividing the box is at seven hundred minutes. Since the majority of the data falls within this range, we can infer that the percentage of students who use 600 to 800 minutes would be quite high.
- % use 600 or fewer minutes:
Since the lower whisker extends down to four hundred minutes and the box ranges from six hundred to eight hundred minutes, we can infer that the percentage of students who use 600 or fewer minutes would be significantly less than 50%. However, without precise data points, we cannot determine the exact percentage.
To summarize:
- % use 800 or more minutes: 0%
- % use 600 to 800 minutes: High percentage
- % use 600 or fewer minutes: Less than 50%
To make inferences about the population from the sample data using the box plot, we can analyze the various components of the plot.
1. Percentage (%) of students who use 800 or more minutes:
Looking at the whisker of the box plot, we can see that it extends up to 1000 minutes. Since the whisker represents the range of the data, we can infer that there is a portion of the population (students) who use 800 or more minutes. However, we cannot determine the exact percentage from the given information.
2. Percentage (%) of students who use 600 to 800 minutes:
The box in the plot represents the middle 50% of the data. In this case, the box spans from 600 to 800 minutes. Therefore, we can infer that approximately 50% of the students in the population use between 600 and 800 minutes.
3. Percentage (%) of students who use 600 or fewer minutes:
Again, looking at the whisker of the box plot, we can see that it extends down to 400 minutes. Since the whisker represents the range of the data, we can infer that there is a portion of the population (students) who use 600 or fewer minutes. However, we cannot determine the exact percentage from the given information.
Note: The box plot gives us a general understanding of the distribution of the data, but without more specific data or measures of spread (such as the interquartile range or standard deviation), we cannot make precise calculations about the population percentages.