Interpreting Percentiles In Exercises 29–32, ...

Question

Interpreting Percentiles In Exercises 29–32, use the ogive, which represents the cumulative frequency distribution for quantitative reasoning scores on the Graduate Record Examination in a recent range of years. (Adapted from Educational Testing Service)

What score represents the 65th percentile? How should you interpret this?

Graph showing the cumulative frequency distribution of quantitative reasoning scores with percentiles marked along the y-axis.

What score represents the 65th percentile? How should you interpret this?

Accepted Answer

All right. Hello, everyone. So this question says, the ogives shown below displays the percentiles of math scores for a sample of students. Which score marks the 50th percentile according to the OGive? What does this percentile indicate? So, first, you can see that the X axis represents the different SAT math scores, whereas the Y axis represents the percentile. Now, first, to find the 50th percentile, that is the median, what you do first is locate the number 50 on the Y axis. So here, once you've identified 50 on the Y axis, from there, You draw a horizontal line. Until you find the point on the ogive. Where that horizontal line crosses it. And then once you've located that point. You would draw a vertical line down to find the corresponding SAT score. So in this case, we can see that the vertical line meets the X axis at 575. So, Because of that, the 50th percentile score is 575. So now, what does that mean? Well, recall that as mentioned earlier, the 50th percentile is the median. So because of that, half of students scored below 575 and the other half scored above it. So now, this brings you to the complete final answer, which reads as follows. 575 is the 50th percentile score, and it is the math score below which 50% of the students scored. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

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