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Answer :
To determine the percentile rank for a height of 69 inches, we need to follow several steps. Here's a detailed, step-by-step solution:
1. List the Heights in Order:
The given heights in increasing order are: 55, 59, 59, 60, 61, 63, 64, 64, 65, 68, 69, 72, 74.
2. Count the Total Number of Heights:
There are a total of 13 heights.
3. Count the Number of Heights Less Than the Height of Interest:
The height of interest is 69 inches. The numbers less than 69 inches in the list are:
55, 59, 59, 60, 61, 63, 64, 64, 65, and 68.
So, there are 10 heights less than 69 inches.
4. Calculate the Percentile Rank:
The formula for calculating the percentile rank is:
[tex]\[
\text{Percentile Rank} = \left( \frac{\text{Number of Values Less Than } x}{\text{Total Number of Values}} \right) \times 100
\][/tex]
Plugging in the values:
[tex]\[
\text{Percentile Rank} = \left( \frac{10}{13} \right) \times 100
\][/tex]
[tex]\[
\text{Percentile Rank} = 0.7692 \times 100
\][/tex]
[tex]\[
\text{Percentile Rank} = 76.92
\][/tex]
5. Round the Percentile Rank to the Hundredths Place:
Since 76.92 is already rounded to the hundredths place, we can use it as our answer.
Therefore, the percentile rank for a height of 69 inches is 76.92.
1. List the Heights in Order:
The given heights in increasing order are: 55, 59, 59, 60, 61, 63, 64, 64, 65, 68, 69, 72, 74.
2. Count the Total Number of Heights:
There are a total of 13 heights.
3. Count the Number of Heights Less Than the Height of Interest:
The height of interest is 69 inches. The numbers less than 69 inches in the list are:
55, 59, 59, 60, 61, 63, 64, 64, 65, and 68.
So, there are 10 heights less than 69 inches.
4. Calculate the Percentile Rank:
The formula for calculating the percentile rank is:
[tex]\[
\text{Percentile Rank} = \left( \frac{\text{Number of Values Less Than } x}{\text{Total Number of Values}} \right) \times 100
\][/tex]
Plugging in the values:
[tex]\[
\text{Percentile Rank} = \left( \frac{10}{13} \right) \times 100
\][/tex]
[tex]\[
\text{Percentile Rank} = 0.7692 \times 100
\][/tex]
[tex]\[
\text{Percentile Rank} = 76.92
\][/tex]
5. Round the Percentile Rank to the Hundredths Place:
Since 76.92 is already rounded to the hundredths place, we can use it as our answer.
Therefore, the percentile rank for a height of 69 inches is 76.92.
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