Answer:
The 25th percentile is 248.
The 70th percentile is 700.
Step-by-step explanation:
The pth percentile is a data value such that at least p% of the data-set is less-than or equal to this data value and at least (100-p)% of the data-set are more-than or equal to this data value.
Arrange the data set in ascending order as follows:
S = {75
, 157
, 224
, 248
, 271
, 381
, 472
, 495
, 586
, 676
, 700
, 723
, 743
, 767
, 1250}
The formula to compute the position of the pth percentile is:
![p^{th} \text{Percentile}=\frac{(n+1)\cdot p}{100}](https://tex.z-dn.net/?f=p%5E%7Bth%7D%20%5Ctext%7BPercentile%7D%3D%5Cfrac%7B%28n%2B1%29%5Ccdot%20p%7D%7B100%7D)
Compute the 25th percentile as follows:
![25^{th} \text{Percentile}=\frac{(15+1)\cdot 25}{100}=4^{th}obs.](https://tex.z-dn.net/?f=25%5E%7Bth%7D%20%5Ctext%7BPercentile%7D%3D%5Cfrac%7B%2815%2B1%29%5Ccdot%2025%7D%7B100%7D%3D4%5E%7Bth%7Dobs.)
The 4th observation from the arranged data set is 248
.
Thus, the 25th percentile is 248.
Compute the 70th percentile as follows:
![70^{th} \text{Percentile}=\frac{(15+1)\cdot 70}{100}\approx 11^{th}obs.](https://tex.z-dn.net/?f=70%5E%7Bth%7D%20%5Ctext%7BPercentile%7D%3D%5Cfrac%7B%2815%2B1%29%5Ccdot%2070%7D%7B100%7D%5Capprox%2011%5E%7Bth%7Dobs.)
The 11th observation from the arranged data set is 700.
Thus, the 70th percentile is 700.