Find the percentile for the data value.
 
Data set: 108 120 112 106 114 116 106 104 111 108 112 122 104 108Data set: 108   120   112   106   114   116   106   104   111   108   112   122   104   108   

110110   

105105​; 

data​ value: 114

To find the percentile of the data value 114 within the given data set, we need to follow these steps:

### 1. Organize the Data
First, arrange the data values in ascending order.

Data set:  
104, 104, 104, 105, 106, 106, 108, 108, 108, 110, 111, 112, 112, 114, 116, 120, 122

### 2. Identify the Position of the Data Value
Find the position of 114 in the sorted list. The data value 114 is at position 14 (since it is the 14th value in the sorted list).

### 3. Apply the Percentile Formula
The formula for calculating the percentile of a data value \( x \) is:

\[
P = \frac{L}{N} \times 100
\]

Where:
- \( P \) is the percentile of the data value,
- \( L \) is the number of values less than the data value,
- \( N \) is the total number of data values.

In our case:
- \( L = 13 \) (since 13 values are less than 114),
- \( N = 17 \) (the total number of data points in the set).

Now, calculate the percentile:

\[
P = \frac{13}{17} \times 100 \approx 76.47
\]

### 4. Interpretation
The percentile for the data value 114 is approximately **76.47**. This means that 114 is greater than about 76.47% of the values in the data set.

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Would you like more details or have any other questions?

Here are 5 related questions to expand on this:
1. How do percentiles relate to quartiles?
2. Can you explain how to calculate the median of this data set?
3. What is the difference between a percentile and a percentage?
4. How would you calculate the percentile for a different value, such as 108?
5. How can we interpret data that is at the 50th percentile?

**Tip**: Percentiles are especially useful in understanding how a data point compares to the rest of the data in a distribution.

Find the percentile for the data value.

Data set: 108 120 112 106 114 116 106 104 111 108 112 122 104 108

Data value: 114

Learn how to calculate the percentile of a data value in a given data set. In this problem, we determine the percentile of the value 114 in a data set of 17 values using the percentile formula. Suitable for students in Grades 6-8.

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