Chapter 2.1, Problem 2E

(a)

To determine

Percentile for Colorado with 10.1% of the residents are aged 65 and above.

Answer to Problem 2E

Percentile for Colorado with 10.1% of the residents is 8^th percentile.

Explanation of Solution

Given information:

Stemplot of the percents:

  

Let

n , Number of data values that are less than the individual’s data value

N , Total number of data values

Now,

Write down all the data values from stemplot in ascending order:

Where,

  $7|0\text{represents}7.0$ .

7.0, 8.8, 9.8, 10.0, 10.1, 10.9, 11.1, 11.6, 11.7, 11.7, 11.7, 12.0, 12.1, 12.1, 12.2, 12.2, 12.4, 12.5, 12.6, 12.7, 12.7, 12.8, 12.9, 12.9, 12.9, 13.0, 13.0, 13.0, 13.1, 13.2, 13.2, 13.3, 13.3, 13.4, 13.4, 13.4, 13.5, 13.5, 13.6, 13.8, 13.9, 14.0, 14.2, 14.3, 14.5, 14.6, 14.8, 15.2, 15.4, 16.9.

Note that

4 of the 50 states have percentage below 10.1%.

Percentile can be determined as the number of data values that are less than the individual’s data value ( n ), divided by the total number of data values ( N ), written as percentage.

  $\begin{array}{l}\text{Percentile}=\frac{4}{50}\times 100\%\\ =0.08\times 100\%\\ =8\%\end{array}$

Thus,

Percentile that corresponds with 10.1% of the residents is 8^th percentile.

(b)

To determine

Interpretation of 80^th percentile and percent of Rhode Island’s residents are aged 65 and above.

Answer to Problem 2E

14% of Rhode Island’s residents are 65 or older and is at 80^th percentile.

Explanation of Solution

Given information:

Stemplot of the percents:

  

Let

n , Number of data values that are less than the individual’s data value

N , Total number of data values

Now,

Write down all the data values from stemplot in ascending order:

Where,

  $7|0\text{represents}7.0$ .

7.0, 8.8, 9.8, 10.0, 10.1, 10.9, 11.1, 11.6, 11.7, 11.7, 11.7, 12.0, 12.1, 12.1, 12.2, 12.2, 12.4, 12.5, 12.6, 12.7, 12.7, 12.8, 12.9, 12.9, 12.9, 13.0, 13.0, 13.0, 13.1, 13.2, 13.2, 13.3, 13.3, 13.4, 13.4, 13.4, 13.5, 13.5, 13.6, 13.8, 13.9, 14.0, 14.2, 14.3, 14.5, 14.6, 14.8, 15.2, 15.4, 16.9.

Note that

In the sample, there are total 50 states (or 50 data values).

Such that

  $N=50$

The data value represented by the x^th percentile has x% of the data values below it.

If Rhode Island’s is at 80^th percentile,

80^th percentile has 80% of the data values below it.

Calculate 80% of 50 data values:

  $n=80\%\times N=\frac{80}{100}\times 50=\frac{4}{5}\times 50=40$

We have

40 out of 50 data values below 80^th percentile.

80^th percentile needs to be the 41^st data value in the ascending order, and that is 14.0.

Thus,

In Rhode Island’s, 14% of residents are 65 or older and is at 80^th percentile.