The points scored on a test for a sample of 51 students are summarized in the following table

Oct 13, 2025 by miodeya.com 138 views

The points scored on a test for a sample of 51 students are summarized in the following table

Introduction

Understanding the Problem The points scored on a test for a sample of 51 students are summarized in the following table. This table provides a snapshot of the distribution of scores among the students. The table is divided into different categories based on the score, and the number of students in each category is also provided. In this discussion, we will explore the distribution of scores and calculate the mean, median, and mode of the scores.

The Table

Number of students	Score for each student
9	90
17	80
15	70
10	60

Calculating the Mean

Calculating the Mean To calculate the mean, we need to multiply the number of students in each category by the score and add them up. Then, we divide the sum by the total number of students.

Let's calculate the sum of the products of the number of students and their scores:

9 x 90 = 810 17 x 80 = 1360 15 x 70 = 1050 10 x 60 = 600

The sum of the products is 810 + 1360 + 1050 + 600 = 3820.

Now, we divide the sum by the total number of students, which is 51.

Mean = 3820 / 51 = 74.9

Calculating the Median

Calculating the Median To calculate the median, we need to arrange the scores in ascending order and find the middle value. Since there are 51 students, the middle value is the 26th score.

Let's arrange the scores in ascending order:

60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80,
The points scored on a test for a sample of 51 students are summarized in the following table

Q&A

Q: What is the purpose of the table? A: The table provides a snapshot of the distribution of scores among the students.

Q: How many students are in the sample? A: There are 51 students in the sample.

Q: What is the mean score of the students? A: The mean score is 74.9.

Q: How was the mean score calculated? A: The mean score was calculated by multiplying the number of students in each category by the score and adding them up. Then, the sum was divided by the total number of students.

Q: What is the median score of the students? A: The median score is the middle value of the scores when arranged in ascending order.

Q: How was the median score calculated? A: The median score was calculated by arranging the scores in ascending order and finding the middle value.

Q: What is the mode of the scores? A: The mode is the score that appears most frequently in the table.

Q: How was the mode calculated? A: The mode was calculated by identifying the score that appears most frequently in the table.

Q: What is the significance of the mean, median, and mode in this context? A: The mean, median, and mode provide a summary of the distribution of scores among the students. They can be used to understand the central tendency of the data and to make inferences about the population.

Q: What are some potential limitations of using the mean, median, and mode in this context? A: Some potential limitations include the fact that the data may be skewed or have outliers, which can affect the accuracy of the mean, median, and mode. Additionally, the sample size may be too small to be representative of the population.

Q: How can the mean, median, and mode be used in real-world applications? A: The mean, median, and mode can be used in a variety of real-world applications, such as education, business, and healthcare. For example, they can be used to evaluate student performance, track employee productivity, or monitor patient outcomes.

Conclusion

In conclusion, the points scored on a test for a sample of 51 students are summarized in the following table. The mean, median, and mode provide a summary of the distribution of scores among the students. They can be used to understand the central tendency of the data and to make inferences about the population. However, there are potential limitations to using the mean, median, and mode, and they should be used in conjunction with other statistical methods to gain a more complete understanding of the data.

References

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Glossary

Mean: The average value of a set of data.
Median: The middle value of a set of data when arranged in ascending order.
Mode: The value that appears most frequently in a set of data.
Central tendency: A measure of the middle or average value of a set of data.
Skewed data: Data that is not normally distributed, with some values being much higher or lower than the rest.
Outliers: Values that are significantly higher or lower than the rest of the data.