Question

the stemplot shows the percentages of residents aged 65 and older in the 50 states: 7|0 8|8 9|8 10|0 1 9 11|1 6 7 7 7 12|0 1 1 2 2 4 5 6 7 7 8 9 9 9 13|0 0 0 1 2 2 3 3 4 4 4 5 5 6 8 9 14|0 2 3 5 6 8 15|2 4 16|9 key: 15|2 represents a state for which 15.2% of the residents are age 65 or older. what is the percentile for colorado, where 10.1% of the residents are aged 65 and older? 10th percentile 90th percentile 92nd percentile 8th percentile

Explanation:

Step1: Count total data points

There are 50 data - points (since there are 50 states).

Step2: Count number of data points less than 10.1

Count the number of values in the stemplot less than 10.1. Values are 7.0, 8.8, 9.8, 10.0. There are 4 values less than 10.1.

Step3: Calculate the percentile

The formula for the percentile $P$ is $P=\frac{k}{n}\times100$, where $k$ is the number of data points less than the value of interest and $n$ is the total number of data points. Substituting $k = 4$ and $n=50$ into the formula, we get $P=\frac{4}{50}\times100 = 8$.

Answer:

8th percentile