Question

Find the values of the 30th and 90th percentiles of the data. Please show your work.

Answer 1

Answer:

30th percentile:109

90th percentile: 188

Step-by-step explanation:

The given data set is:

129, 113, 200, 100, 105, 132, 100, 176, 146, 152

We arrange the data set in ascending order to obtain;

Array= $100,100,105,113,129,132,146,176,200$

The 30th percentile is located at

$(\frac{30}{100}\times 10 )}$ -th position, where n=10 is the number of items in the data set

This implies that the 30th percentile is at the 3rd position.

Since 3 is an integer, the 30th percentile is the average of the 3rd and 4th occurrence in the array;

This implies that the 30th percentile = $\frac{105+113}{2}=\frac{218}{2}=109$

The 90th percentile is located at

$(\frac{90}{100}\times 10 )}$ -th position, where n=10 is the number of items in the data set

This implies that the 90th percentile is at the 9th position.

Since 9 is an integer, the 90th percentile is the average of the 9th and 10th occurrence in the array;

This implies that the 90th percentile = $\frac{176+200}{2}=\frac{376}{2}=188$