The following dotplot represents the heights of 20 randomly selected American men.
Dot plot of heights of 20 men. A line dividing the dot plot appears at 70 inches. To the left of the line are 7 dots and a label of 35%. To the right of the line are 13 dots with a label of 65%.
Based on this sample, what would be the percentile for a man who is 70 inches tall? Write a sentence to interpret this percentile.
 Correct
A man who is 70 inches tall would be at the 35th percentile. This means that approximately 35% of men in this sample are shorter than 70 inches.
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Knowing that 15% of the 20 men in this sample is 3 men, at what height would you estimate the 15th percentile to fall?
 inches
Incorrect Not quite. To find the 15th percentile, we need to find a height that cuts off 15% (or equivalently, three dots) below it.

To find the height that corresponds to the 15th percentile, we need to identify a height where exactly 3 men (15% of 20) are shorter than that height.

Since the dot plot divides 20 men into 7 men below 70 inches (the 35th percentile) and 13 men above, the 15th percentile must fall between the heights of the first few men on the lower end of the distribution.

Thus, we estimate that the 15th percentile would be below the height where 3 men have dots on the left side of the plot. This height should be lower than 70 inches but higher than the height of the men represented by the first 2 dots.

Without knowing the exact heights of these men, we can only estimate based on the distribution of the dots. If the dots are spread relatively evenly, we might place the 15th percentile around **68 inches**, where 3 dots (representing 3 men) fall below this height.

### Interpretation:
A man who is at the 15th percentile would be taller than approximately 15% of the men in this sample, meaning that 85% of the men in the sample are taller than he is.

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Would you like further clarification, or do you have any other questions?

Here are 5 related questions for practice:
1. What would be the height at the 50th percentile based on the sample?
2. If 10% of the men are taller than 75 inches, what height would you estimate the 90th percentile to be?
3. How would you find the exact height for the 25th percentile in this data?
4. How could the median be different if the sample size was larger?
5. What conclusions can you draw if the dot plot showed an equal number of dots on either side of 70 inches?

**Tip:** Percentiles are a way to compare values within a data set by showing the percentage of the data that lies below a particular value.

The following dotplot represents the heights of 20 randomly selected American men. Dot plot of heights of 20 men. A line dividing the dot plot appears at 70 inches. To the left of the line are 7 dots and a label of 35%. To the right of the line are 13 dots with a label of 65%. Based on this sample, what would be the percentile for a man who is 70 inches tall? Knowing that 15% of the 20 men in this sample is 3 men, at what height would you estimate the 15th percentile to fall?

Explore how to interpret percentiles in a dot plot showing the heights of 20 men. Learn how to estimate the 15th percentile and understand the percentile rank for a height of 70 inches, which falls at the 35th percentile. This problem is ideal for students in Grades 10-12 studying statistics and data distribution.

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