Question

Thirteen internists in the Midwest are randomly selected, and each internist is asked to report last year's income. The incomes obtained are:

152,000 144,000 162,000 154,000 146,000 241,000 127,000 141,000 171,000 177,000 138,000 132,000 192,000. Find the 90th percentile.

Answer 1

To find the 90th percentile of a set of data, arrange the data in ascending order, calculate the position of the 90th percentile, and take the average of the values at that position and the next lower position.

Step-by-step explanation:

To find the 90th percentile of a set of data, first arrange the data in ascending order. In this case, the incomes are: $127,000, $132,000, $138,000, $141,000, $144,000, $146,000, $152,000, $154,000, $162,000, $171,000, $177,000, $192,000, $241,000. Next, calculate the position of the 90th percentile by multiplying the total number of values (13) by 0.9. This gives us a position of 11.7, which is between the 11th and 12th values in the sorted data set. To find the 90th percentile, take the average of these two values. So, the 90th percentile of the incomes is (154,000 + 162,000)/2 = $158,000.