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Zorluk: KolayPercentiles and Quartiles

A dataset contains 2020 distinct test scores arranged in ascending order:

10,12,15,17,20,22,25,28,30,32,35,38,40,43,45,48,50,52,55,6010, 12, 15, 17, 20, 22, 25, 28, 30, 32, 35, 38, 40, 43, 45, 48, 50, 52, 55, 60

If the pthp\text{th} percentile of a dataset of NN values is defined as the value at position k=p100×Nk = \frac{p}{100} \times N when ordered from least to greatest, what is the 75th75\text{th} percentile of these test scores?

Cevap: 45

Cevap

The 75th percentile of the given test scores is 45.
The 75th percentile corresponds to position k = (75/100) * 20 = 15 in the ordered list of 20 scores, which is equal to 45.

Adım Adım Çözüm

1
Calculate the position index kk for the 75th75\text{th} percentile.
k=75100×20=15k = \frac{75}{100} \times 20 = 15
The rank formula determines the 1-based index of the target percentile value in an ordered set of size N=20N = 20.
2
Locate the 15th15\text{th} score in the ordered dataset.
The 15th15\text{th} score is 4545.
Counting from the lowest score (1010 at position 1), the 15th15\text{th} score in the sequence is 4545.

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Percentiles and Quartiles
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Percentiles and Quartiles

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