(b)Find the third quartile of the scores.

The third quartile of the scores is 

To find the third quartile (Q3) of the scores, follow these steps:

### Step 1: Confirm the data is in ascending order.
This has already been done:

\[ 58, 60, 61, 63, 66, 68, 69, 70, 71, 71, 72, 75, 76, 76, 76, 77, 77, 78, 83, 84, 84, 87, 87, 89, 91, 95, 96, 96, 97, 98 \]

### Step 2: Determine the number of data points (\(n\)).
There are \(n = 30\) data points.

### Step 3: Find the position of Q3.
The third quartile (Q3) is the value at the 75th percentile. The position of Q3 can be found using the formula:

\[
Q3 = \frac{3(n + 1)}{4}
\]

Substituting the value of \(n\):

\[
Q3 = \frac{3(30 + 1)}{4} = \frac{93}{4} = 23.25
\]

### Step 4: Locate Q3.
Since \(Q3\) is at position 23.25, it lies between the 23rd and 24th values in the data set. To find the exact value, we can interpolate between the 23rd and 24th values.

- The 23rd value is 87.
- The 24th value is 89.

The value of Q3 can be found by interpolating between these two values:

\[
Q3 = 87 + 0.25 \times (89 - 87) = 87 + 0.25 \times 2 = 87 + 0.5 = 87.5
\]

### Final Answer:
The third quartile (Q3) of the scores is **87.5**.

Would you like more details on the interpolation process or have any other questions?

Here are five related questions:
1. How do you calculate the interquartile range (IQR) using Q1 and Q3?
2. What is the significance of the third quartile in a data set?
3. How can quartiles help in identifying outliers in a dataset?
4. How would you find the quartiles if the data set had an odd number of observations?
5. What role do quartiles play in box plots?

**Tip:** The third quartile (Q3) represents the value below which 75% of the data falls. It is useful in understanding the spread of the upper half of the dataset.

Learn how to find the third quartile (Q3) of a dataset with a detailed step-by-step guide. Understand the significance of Q3 in statistics and how to interpolate between data points. Suitable for 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