A school randomly selected some 7th grade students and surveyed them on their weights. The results are summarized into the following frequency table. If the school has a total of 1... A school randomly selected some 7th grade students and surveyed them on their weights. The results are summarized into the following frequency table. If the school has a total of 1000 students, predict the number of students whose weight is less than 60kg in the school.
Understand the Problem
The question presents a frequency table and a pie chart summarizing the weights of 7th-grade students. We need to use the given information to predict the number of students whose weight is less than 60kg in the entire school, given that the school has a total of 1000 students.
Answer
720
Answer for screen readers
720
Steps to Solve
- Find the total number of surveyed students
Let $N$ be the total number of students in the sample. From the pie chart, we know that group D represents 20% of the students, and from the frequency table, group D has 40 students. Therefore, we have:
$0.20 \times N = 40$ $N = \frac{40}{0.20} = 200$
- Solve for $m$
The total number of students is the sum of students in each group. So, $N = 12 + m + 80 + 40 + 16 = 200$ $m + 148 = 200$ $m = 200 - 148 = 52$
- Calculate the number of students weighing less than 60kg in the sample
The groups representing students weighing less than 60kg are groups A, B, and C. The number of students in these groups are 12, 52, and 80, respectively. So, the total number of students weighing less than 60kg in the sample is: $12 + 52 + 80 = 144$
- Calculate the proportion of students weighing less than 60kg in the sample
The proportion is the number of students weighing less than 60kg divided by the total number of students in the sample: $\frac{144}{200} = \frac{72}{100} = 0.72$
- Predict the number of students weighing less than 60kg in the entire school
Since the school has 1000 students, we multiply the proportion (0.72) by the total number of students: $0.72 \times 1000 = 720$
720
More Information
The question uses the concept of proportions to scale the sample data to the entire school population. By computing the number of students less than 60kg in our sample, we can scale the data up to the total population size to get an estimate of the total number of students less than 60kg.
Tips
- Incorrectly calculating the total number of surveyed students $N$.
- Incorrectly calculating $m$
- Not considering all groups (A, B, and C) when calculating the number of students weighing less than 60kg in the sample
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