The ogive represents the heights of males in a  particular country in the​ 20-29 age group. What height represents the 9090 Superscript th​ percentile? How should you interpret​ this?
63
65
67
69
71
73
75
0
20
40
60
80
100
Height (in inches)
Percentile
 


An Ogive has a horizontal axis labeled Height (in inches) from 63 to 76 in increments of 1 and a vertical axis labeled Percentile from 0 to 100 in increments of 10. The graph consists of fourteen plotted points connected by line segments from left to right. The coordinates of the plotted points are at (63, 0), (64, 4), (65, 8), (66, 13), (67, 20), (68, 34), (69, 43), (70, 60), (71, 69), (72, 79), (73, 89), (74, 94), (75, 98), and (76, 100).
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Part 1
The 90th  percentile represents about enter your response here inches.
​(Round to nearest whole number as​ needed.)

The 90th percentile is where 90% of the values fall below a given point. To estimate the height representing the 90th percentile from the ogive, we need to find the corresponding height where the percentile is closest to 90%.

Based on the provided points:
- At \( \text{Height} = 73 \), Percentile = 89
- At \( \text{Height} = 74 \), Percentile = 94

Since the 90th percentile lies between these two points, we can interpolate between them to estimate the height at the 90th percentile.

### Interpolation:

Using linear interpolation, the formula is:
\[
\text{Height at 90th percentile} = 73 + \frac{90 - 89}{94 - 89} \times (74 - 73)
\]

Simplifying:
\[
\text{Height at 90th percentile} = 73 + \frac{1}{5} \times 1 = 73 + 0.2 = 73.2
\]

So, the 90th percentile corresponds to approximately **73 inches** (rounded to the nearest whole number).

### Interpretation:
The interpretation of this result is that 90% of males in the 20-29 age group in this country are shorter than or equal to **73 inches** (6 feet 1 inch), and 10% are taller.

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Would you like further details or have any questions?

Here are 5 related questions to explore further:
1. What is the 50th percentile (median) height from this ogive?
2. How can you calculate the interquartile range from an ogive?
3. What does the slope of an ogive at a specific height indicate about the distribution of heights?
4. How would you construct an ogive from raw height data?
5. What is the significance of the 10th percentile in this context?

**Tip:** Always ensure that the ogive graph is smooth and properly labeled for easier interpretation.

The ogive represents the heights of males in a particular country in the 20-29 age group. What height represents the 90th percentile? How should you interpret this? The ogive graph is labeled with heights in inches from 63 to 76 and percentiles from 0 to 100. Key points include (63, 0), (64, 4), (65, 8), (66, 13), (67, 20), (68, 34), (69, 43), (70, 60), (71, 69), (72, 79), (73, 89), (74, 94), (75, 98), and (76, 100). What is the height at the 90th percentile?

Learn how to find the 90th percentile height from an ogive graph representing the heights of males in the 20-29 age group. This solution involves using linear interpolation between key data points (73, 89) and (74, 94) to estimate the 90th percentile at approximately 73 inches. This method is suitable for students in Grades 9-12.

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