Question

Where do the young live? Here is a stemplot of the percent of residents aged 25 to 34 in each of the 50 states:

Part (a). Why did we split stems?

Part (b). Give an appropriate ate key for this stemplot.

Part (c). Describe the shape of the distribution. Are there any outliers?

Short answer

Part (a) we were able to determine the general shape of the distribution.

Part (b) Key: $\overline{)16}0$represents a state that has 16.0% residents aged 25 to 34

Part (c)

Roughly symmetric

16.0% is a possible outlier.

Step-by-step solution

Part (a) Step 1. Given information. 

Stem	Leaf
11	44
11	66778
12	0134
12	666778888
13	0000001111444
13	7788999
14	0044
14	567
15	11
15
16	0

Part (a) Step 2. Did we split stem 

Stem	Leaf
11	44
11	66778
12	0134
12	666778888
13	0000001111444
13	7788999
14	0044
14	567
15	11
15
16	0

Key: $\overline{)11}4$means 11.4%

If we had not split the stems, all data values would have been placed on only six stems (11, 12, 13, 14, 15, 16), making it difficult to determine the general shape of the distribution.

As a result, we divided the stems in order to determine the general shape of the distribution.

Part (b) Step 1. Give an appropriate ate key for this stemplot.  

The data values represent the percentage of residents aged 25 to 34 in each of the 50 states, according to what we've been told.

Let us use the key with the largest data value, which is given at the bottom of the stemplot and is thus 1610. Because the percentage must be between 0% and 100%, this most likely means that the corresponding state has 16.0 percent residents aged 25 to 34. (and as 1.60 percent is probability to small a percentage).

The following is a possible key:

Key: The state of $\overline{)16}0$has 16.0 percent of its residents aged 25 to 34.

Part (c) Step 1. The shape of the distribution Are there any outliers 

Because most of the data values appear to lie roughly in the middle of the stemplot, the distribution has a roughly symmetric shape.

There is a gap in the stemplot between 1610 (which represents 16.0 percent) and the other data values in the stemplot, implying that 16.0 percent could be an outlier.

As a results:

Roughly symmetric

16.0% is a possible outlier.