his means that approximately 
% of the data lie at or below 
, when the data are ranked.
11	47	86	33	39	44	28	104	71	103	43	54	80	42


To determine the percentage of data that lie at or below a certain value when the data are ranked, we need to follow these steps:

1. **Rank the data**: Arrange the numbers in ascending order.
2. **Identify the position**: Locate the value of interest in the ranked data.
3. **Calculate the percentage**: Use the formula for percentile, which is \(\frac{ \text{Position of the value}}{\text{Total number of data points}} \times 100\%\).

Let's go through the steps with the given dataTo determine the percentage of data that lie at or below a certain value when the data are ranked, we need to follow these steps:

1. **Rank the data**: Arrange the numbers in ascending order.
2. **Identify the position**: Locate the value of interest in the ranked data.
3. **Calculate the percentage**: Use the formula for percentile, which is \(\frac{ \text{Position of the value}}{\text{Total number of data points}} \times 100\%\).

Let's go through the steps with the given 

### 1. Rank the Data:
First, let's rank the data in ascending order:

\[ 11, 28, 33, 39, 42, 43, 44, 47, 54, 71, 80, 86, 103, 104 \]

### 2. Identify the Position:
For example, if we want to determine the percentage of data that lie at or below the value 47:

- 47 is the 8th value in the ranked data.

### 3. Calculate the Percentage:
- There are 14 data points in total.
- The percentage of data that lies at or below 47 is:

\[
\frac{8}{14} \times 100\% = \frac{4}{7} \times 100\% \approx 57.14\%
\]

So, approximately 57.14% of the data lie at or below 47.

Would you like details on any specific part of this process or have other questions?

---

Here are 5 related questions:

1. How would you find the median of this dataset?
2. What is the 75th percentile (third quartile) in this data?
3. How do you calculate the interquartile range (IQR) for this dataset?
4. What is the difference between percentiles and quartiles?
5. How would outliers affect the percentile calculation in a dataset?

**Tip:** Understanding how to calculate percentiles can help you interpret data distributions and variability more effectively.

Learn how to calculate percentiles step-by-step with example data. Understand how to determine the percentage of data that lie at or below a certain value when the data are ranked. Suitable for students in Grades 9-12 studying statistics.

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