https://file.aiquickdraw.com/mathbot/file/17291752650936e9025qe.jpg

Let's analyze the question.

The scores are: **96, 77, 86, 97, 89**. We need to determine which of the provided statements is true. To do this, we will calculate the necessary measures of center (mode, mean, median).

### Step 1: Mode
The **mode** is the number that appears most frequently in the data set. In this case, all the scores appear only once, so there is no mode. Thus, the statement "The mode of the set of scores is 96" is false.

### Step 2: Mean
The **mean** is the average of the scores. To calculate it:

\[
\text{Mean} = \frac{96 + 77 + 86 + 97 + 89}{5} = \frac{445}{5} = 89
\]

So, the mean is **89**.

### Step 3: Median
To find the **median**, we first arrange the scores in ascending order:

\[
77, 86, 89, 96, 97
\]

Since there are 5 numbers, the median is the middle number, which is **89**.

### Step 4: Analyze the statements
- **Statement 1:** "The mode of the set of scores is 96." — **False** (no mode exists).
- **Statement 2:** "The mean of the set is less than the median." — **False** (mean and median are both 89, so they are equal, not less than).
- **Statement 3:** "The mean and the median of the set of scores are the same." — **True** (both are 89).
- **Statement 4:** "The median of the set of scores is 86." — **False** (the median is 89, not 86).

Thus, the correct answer is **"The mean and the median of the set of scores are the same."**

Would you like more details or have any questions?

### Related questions:
1. How would the mean and median change if the highest score were removed?
2. How do you find the mode if there is no repeating number?
3. What happens to the median if a sixth number is added to this set?
4. Can a data set have more than one mode?
5. What are other examples where the mean and median are the same?

### Tip:
When calculating the mean and median, arranging numbers in order first simplifies finding the median!

Bernice received the following scores on five science tests: 96, 77, 86, 97, and 89. Which of the following statements is true?

Learn how to determine the mean, median, and mode of a set of scores from five science tests (96, 77, 86, 97, 89). This solution guides you through calculating central tendencies and analyzing the correct true statement. Ideal for middle school students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation