Q: A pie chart is constructed to represent the distribution of student loan balances among borrowers. If the relative frequencies are 12.7% for $$10,001 to$$ $$25,000$$, 40% for $$1 to$$ $$10,000$$, 32.6% for $$25,001 to$$ $$50,000$$, and 14.8% for $$50,001 or $$more, what is the central angle for the $$25,001 to$$ $$50,000$$ category?

$$32.6\% \times 360$$^{\circ}$$ = 117.36$$^{\circ}$$

Q: A pie chart is used to display the distribution of house types in a town: Cape 35%, Garrison 20%, Split 45%. What is the central angle for the Split category?

$$45\% \times 360$$^{\circ}$$ = 162$$^{\circ}$$

Q: If a stem-and-leaf plot for incomes (in millions) has stems from 3 to 8, and the leaves for stem 6 are 4, 7, 8, what is the range of incomes represented by stem 6?

$$64$$\text{ million to }68\text{ million}$

Q: A pie chart is constructed for a poll about health insurance satisfaction: Very 15%, Somewhat 28%, Not at all 35%, No opinion 22%. What is the central angle for the 'Somewhat' category?

$$28\% \times 360$$^{\circ}$$ = 100.8$$^{\circ}$$

Question 1

A stem-and-leaf plot is constructed for the following exam scores: 62, 75, 80, 87, 67, 82, 88, 96, 91, 75, 89, 85, 69. What is the correct stem-and-leaf plot for this data set?

Accepted Answer

$$6 \mid 2\ 7\ 9$$
$$7 \mid 5\ 5\ 0$$
$$8 \mid 2\ 7\ 8\ 9\ 5$$
$$9 \mid 1\ 6$$

Question 2

Given the stem-and-leaf plot below for hours worked by nurses:
$$2 \mid 2\ 2\ 3\ 3\ 3\ 6\ 6\ 9$$
$$3 \mid 0\ 0\ 0\ 2\ 2\ 2\ 2\ 2\ 2\ 6\ 8$$
$$4 \mid 0\ 0\ 0\ 5\ 6\ 6\ 9$$
What best describes the distribution of hours worked?

Accepted Answer

Most nurses work between 30 and 40 hours per week, inclusive.

Question 3

A pie chart is constructed to represent the distribution of student loan balances among borrowers. If the relative frequencies are 12.7% for $$10,001 to$$ $$25,000$$, 40% for $$1 to$$ $$10,000$$, 32.6% for $$25,001 to$$ $$50,000$$, and 14.8% for $$50,001 or $$more, what is the central angle for the $$25,001 to$$ $$50,000$$ category?

Accepted Answer

$$32.6\% 	imes 360$$^{\circ}$$ = 117.36$$^{\circ}$$

Question 4

In a stem-and-leaf plot, what does the 'stem' represent?

Accepted Answer

The leftmost digit(s) of each data value.

Question 5

A pie chart shows beverage sizes chosen at a restaurant: Small 15%, Medium 8%, Large 31%, XL 46%. What percentage of customers choose a medium-sized beverage?

Accepted Answer

$$8\%$$

Question 6

Given the following stem-and-leaf plot for incomes (in millions):
$$3 \mid 344$$
$$4 \mid 245$$
$$5 \mid 556$$
$$6 \mid 478$$
$$7 \mid 38$$
$$8 \mid 1$$
What best describes the distribution of incomes?

Accepted Answer

Most of the incomes are less than 60 million dollars.

Question 7

If a stem-and-leaf plot has stems from 2 to 5 and the leaves for stem 3 are: 0, 0, 0, 2, 2, 2, 2, 2, 2, 6, 8, what is the median value in the data set?

Accepted Answer

$$32$$

Question 8

A pie chart is constructed from the following poll results about satisfaction with health insurance: Very 15%, Somewhat 28%, Not at all 35%, No opinion 22%. Which category has the largest sector in the pie chart?

Accepted Answer

Not at all

Question 9

When constructing a stem-and-leaf plot, what is the minimum number of rows required if the smallest value is 29 and the largest is 59?

Accepted Answer

$$4 ($$stems: 2, 3, 4, 5)

Question 10

A pie chart is used to display the distribution of house types in a town: Cape 35%, Garrison 20%, Split 45%. What is the central angle for the Split category?

Accepted Answer

$$45\% 	imes 360$$^{\circ}$$ = 162$$^{\circ}$$

Question 11

If a stem-and-leaf plot for exam scores has stems 7, 8, and 9, and the leaves for stem 8 are 2, 5, 7, 8, 9, what is the highest exam score in the data set?

Accepted Answer

$$95$$

Question 12

A pie chart is constructed for student loan balances. If the largest sector represents $$1 to$$ $$10,000$$ balances, what does this indicate about the distribution?

Accepted Answer

Most student loan balances are $$1 to$$ $$10,000.$$

Question 13

In a stem-and-leaf plot, if the key is $$2 \mid 7 = 27$$, what does the leaf '7' represent?

Accepted Answer

The digit 7 in the ones place.

Question 14

A pie chart for beverage sizes at a restaurant shows: Small 15%, Medium 8%, Large 31%, XL 46%. Which size is the least popular?

Accepted Answer

Medium

Question 15

If a stem-and-leaf plot for incomes (in millions) has stems from 3 to 8, and the leaves for stem 6 are 4, 7, 8, what is the range of incomes represented by stem 6?

Accepted Answer

$$64$$	ext{ million to }68	ext{ million}$

Question 16

A pie chart is constructed for a poll about health insurance satisfaction: Very 15%, Somewhat 28%, Not at all 35%, No opinion 22%. What is the central angle for the 'Somewhat' category?

Accepted Answer

$$28\% 	imes 360$$^{\circ}$$ = 100.8$$^{\circ}$$

Question 17

If a stem-and-leaf plot for exam scores has stems 6, 7, 8, and 9, and the leaves for stem 7 are 0, 5, 5, what is the mean of the scores represented by stem 7?

Accepted Answer

$$\frac{70 + 75 + 75}{3} = 73.33$$

Question 18

A pie chart is constructed for house types in a town: Cape 35%, Garrison 20%, Split 45%. Which house type is the least common?

Accepted Answer

Garrison

Question 19

If a stem-and-leaf plot for hours worked by nurses has stems 2, 3, 4, and the leaves for stem 4 are 0, 0, 0, 5, 6, 6, 9, what is the mode of the hours worked?

Accepted Answer

$$40$$

Stem-and-Leaf Plots and Pie Charts in Descriptive Statistics

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