Given the following data, find the weight that represents the 85th percentile.
Weights of Newborn Babies
7.7
8.1
9.3
7.7
8.0
6.7
7.7
6.4
6.5
7.7
7.7
6.3
8.6
5.5
7.2

To find the weight that represents the 85th percentile, we follow these steps:

1. **Organize the data** in ascending order.
2. **Calculate the position** of the 85th percentile using the formula:
   \[
   P = \frac{n \times k}{100}
   \]
   where \( P \) is the position, \( n \) is the total number of data points, and \( k \) is the percentile (in this case, 85).

3. **Locate the value** at the calculated position.

### Step 1: Organize the Data
Let's organize the weights in ascending order:

\[ 5.5, 6.3, 6.4, 6.5, 6.7, 7.2, 7.7, 7.7, 7.7, 7.7, 7.7, 8.0, 8.1, 8.6, 9.3 \]

### Step 2: Calculate the Position
The number of data points (\( n \)) is 15.

The position for the 85th percentile is calculated as follows:

\[
P = \frac{15 \times 85}{100} = 12.75
\]

Since 12.75 is not a whole number, we round up to the next whole number, which is 13. This means we should look at the 13th value in the ordered list.

### Step 3: Locate the 85th Percentile Value
The 13th value in the sorted list is **8.1**.

Thus, the weight that represents the 85th percentile is **8.1** pounds.

Would you like further details or have any questions?

---

Here are 5 related questions you might find interesting:
1. How do you calculate the median from a data set?
2. What is the interquartile range, and how is it determined?
3. Can you explain the difference between percentiles and quartiles?
4. How do you find the mean and standard deviation for this data set?
5. What are some common applications of percentiles in real-world scenarios?

**Tip:** When working with percentiles, always ensure the data is correctly ordered and consider whether interpolation is needed when dealing with non-integer positions.

Discover how to find the weight that represents the 85th percentile from a dataset of newborn babies' weights. This problem involves calculating percentiles and organizing data points. Suitable for high school students studying statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation