https://file.aiquickdraw.com/mathbot/file/17275591537893vy27qp1.jpg

Let's work through the questions step by step using the frequency table and the provided information:

### a. What is the sample size?

The sample size is the total number of students. To find it, we sum up the frequencies of all the score ranges. The relative frequency is the proportion of students in each range, and we can find the actual frequency by multiplying the relative frequency by the sample size.

Given that the sum of all frequencies must equal the sample size, let's start by calculating the frequencies.

#### b. Find the missing relative frequency.

The sum of relative frequencies should be 1 (or 100%). To find the missing relative frequency, subtract the sum of the other relative frequencies from 1.

#### c. How many students in the sample had a score less than 60?

This includes the score ranges 30-39, 40-49, and 50-59. We calculate the number of students in these ranges by summing up the frequencies for these categories.

#### d. How many students in the sample had a score more than 60?

This includes the score ranges 60-69, 70-79, 80-89, and 90-99. Again, we sum up the frequencies for these categories.

#### e. How many students in the sample had a score at least 80?

This includes the score ranges 80-89 and 90-99. We sum up the frequencies for these categories.

#### f. Obtain midpoints of the classes and use it to compute the mean test score for the sample.

The midpoint for each class can be found by taking the average of the lower and upper bounds of the score range. Then, multiply each midpoint by its corresponding frequency, sum those products, and divide by the total sample size to get the mean.

#### g. If there are 2,100 students in all the introductory statistics classes, estimate how many students scored between 60 and 79 in the test.

We can calculate the proportion of students who scored between 60 and 79 in the sample and apply this proportion to the total number of students (2,100).

Let me calculate this for you now.Here are the answers to the questions based on the calculations:

### a. What is the sample size?
The sample size is 50 students.

### b. Find the missing relative frequency.
The missing relative frequency is approximately **0.20**.

### c. How many students in the sample had a score less than 60?
There are **6 students** who had a score less than 60.

### d. How many students in the sample had a score more than 60?
There are **34 students** who had a score more than 60.

### e. How many students in the sample had a score at least 80?
There are **12 students** who had a score of at least 80.

### f. Obtain midpoints of the classes and use it to compute the mean test score for the sample.
The mean test score is approximately **56.8**.

### g. If there are 2,100 students in all the introductory statistics classes, estimate how many students scored between 60 and 79 in the test.
Approximately **924 students** scored between 60 and 79 in the total population of 2,100 students.

Would you like more details on any of the steps? Do you have further questions?

### Follow-up questions:
1. How would you calculate the median score for this sample?
2. What would be the effect of a higher sample size on the accuracy of these estimates?
3. How can you interpret the standard deviation based on this distribution?
4. What if the relative frequencies were different? How would that affect the mean score?
5. How can we estimate the probability of a student scoring above 80?

**Tip**: To improve accuracy in future statistical analysis, consider using larger sample sizes, as they tend to reduce variability and give more reliable estimates.

Following frequency table shows the test score distribution of a sample of 50 students in an introductory statistics class. Based on this table, answer the following questions: What is the sample size? Find the missing relative frequency. How many students in the sample had a score less than 60? How many students in the sample had a score more than 60? How many students in the sample had a score at least 80? Obtain midpoints of the classes and use it to compute the mean test score for the sample. If there are 2100 students in all the introductory statistics classes, estimate how many students scored between 60 and 79 in the test.

Analyze the test score distribution of a sample of 50 students using a frequency table. Calculate the missing relative frequency, number of students in different score ranges, and estimate mean scores. Understand key statistical concepts such as relative frequency and midpoints. Suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation