Question

The report "Progress for Children" (UNICEF, April 2005) included the accompanying data on the percentage of primary-school-age children who were enrolled in school for 19 countries in Northern Africa and for 23 countries in Central Africa.

Northern Africa

54.6	34.3	48.9	77.8	59.6	88.5	97.4	92.5	83.9	96.9	88.9
98.8	91.6	97.8	96.1	92.2	94.9	98.6	86.6

Central Africa

58.3	34.6	35.5	45.4	38.6	63.8	53.9	61.9	69.9	43.0	85.0
63.4	58.4	61.9	40.9	73.9	34.8	74.4	97.4	61.0	66.7	79.6
98.9

We will construct a comparative stem-and-leaf display using the first digit of each observation as the stem and the remaining two digits as the leaf. To keep the display simple the leaves will be truncated to one digit. For example, the observation 54.6 would be processed as

54.6 → stem = 5, leaf = 4 (truncated from 4.6),

the observation 96.1 would be processed as

96.1 → stem = ? , leaf = ? (truncated from 6.1)

and the observation 35.5 would be processed as

35.5 → stem = ? , leaf = ?(truncated from 5.5).

The resulting comparative stem-and-leaf display is shown in the figure below.

Comparative stem-and-leaf display for percentage of children enrolled in primary school.

Stem: Tens
Leaf: Ones

Central Africa		Northern Africa
4854	3	4
035	4	8
838	5	49
6113913	6
943	7	76
5	8	8386
87	9	7268176248

From the comparative stem-and-leaf display we can see that there is quite a bit of variability in the percentage enrolled in school for both Northern and Central African countries and that the shapes of the two data distributions are quite different. The percentage enrolled in school tends to be higher in Northern African countries than in Central African countries, although the smallest value in each of the two data sets is about the same. For Northern African countries the distribution of values has a single peak in the 90s with the number of observations declining as we move toward the stems corresponding to lower percentages enrolled in school. For Central African countries the distribution is more symmetric, with a typical value in the mid 60s.

How many individual stem-and-leaf displays are represented by the comparative stem-and-leaf display?

-one

-two     

-three

-It can't be represented as simple stem-and-leaf display.

Answer 1

The report "Progress for Children" (UNICEF, April 2005) included the accompanying data on the percentage of primary-school-age children who were enrolled in school for 19 countries in Northern Africa and for 23 countries in Central Africa.

Northern Africa
54.6	34.3	48.9	77.8	59.6	88.5	97.4	92.5	83.9	96.9	88.9
98.8	91.6	97.8	96.1	92.2	94.9	98.6	86.6

Central Africa
58.3	34.6	35.5	45.4	38.6	63.8	53.9	61.9	69.9	43.0	85.0
63.4	58.4	61.9	40.9	73.9	34.8	74.4	97.4	61.0	66.7	79.6
98.9

We will construct a comparative stem-and-leaf display using the first digit of each observation as the stem and the remaining two digits as the leaf. To keep the display simple the leaves will be truncated to one digit. For example, the observation 54.6 would be processed as

54.6 → stem = 5, leaf = 4 (truncated from 4.6),

the observation 96.1 would be processed as

96.1 → stem = 9 , leaf = 6 (truncated from 6.1)

and the observation 35.5 would be processed as

35.5 → stem = 3 , leaf = 5(truncated from 5.5).

The resulting comparative stem-and-leaf display is shown in the figure below.

Comparative stem-and-leaf display for percentage of children enrolled in primary school.

Stem: Tens Leaf: Ones
Central Africa		Northern Africa
4854	3	4
035	4	8
838	5	49
6113913	6
943	7	76
5	8	8386
87	9	7268176248

From the comparative stem-and-leaf display we can see that there is quite a bit of variability in the percentage enrolled in school for both Northern and Central African countries and that the shapes of the two data distributions are quite different. The percentage enrolled in school tends to be higher in Northern African countries than in Central African countries, although the smallest value in each of the two data sets is about the same. For Northern African countries the distribution of values has a single peak in the 90s with the number of observations declining as we move toward the stems corresponding to lower percentages enrolled in school. For Central African countries the distribution is more symmetric, with a typical value in the mid 60s.

How many individual stem-and-leaf displays are represented by the comparative stem-and-leaf display?

-one

Answer: -two     

-three

-It can't

be represented as simple stem-and-leaf display.

Note: In two-sided stem-and-leaf plots, which are also often called back-to-back stem-and-leaf plots, two individual stem-and-leaf displays are represented.