Q: A pie chart is used to display the results of a survey on flu prevention methods. If 61% of respondents chose 'Washing your hands,' what is the central angle for this sector in the pie chart? Use $$ \text{Angle} = \text{Percentage} \times 360^\circ .$$

$$ 0.61 \times 360^\circ = 219.6^\circ $$

Question 1

A physical therapist collects data on the body part requiring rehabilitation for 30 patients. Which type of data is this, and what is the most appropriate graphical display to summarize it?

Accepted Answer

Qualitative data; bar graph

Question 2

Given the frequency distribution for body part injuries: Back (12), Wrist (2), Elbow (1), Hip (2), Shoulder (4), Knee (5), Hand (2), Groin (1), Neck (1), what is the relative frequency for 'Shoulder' injuries? Use the formula $$ 	ext{Relative Frequency} = \frac{	ext{Frequency}}{	ext{Total Observations}} .$$

Accepted Answer

$$ \frac{4}{30} = 0.1333 $$

Question 3

A pie chart is used to display the results of a survey on flu prevention methods. If 61% of respondents chose 'Washing your hands,' what is the central angle for this sector in the pie chart? Use $$ 	ext{Angle} = 	ext{Percentage} 	imes 360^\circ .$$

Accepted Answer

$$ 0.61 	imes 360^\circ = 219.6^\circ $$

Question 4

A researcher surveys 40 households for the number of televisions. Is this data discrete or continuous, and why?

Accepted Answer

Discrete, because the number of televisions can only take specific integer values.

Question 5

Given the following class limits for a frequency distribution: Lower limits: 32, 36, 40, 44, 48. What is the class width?

Accepted Answer

$$ 36 - 32 = 4 $$

Question 6

A histogram of SAT scores is bell-shaped and symmetric. Which of the following statements is true about the mean, median, and mode?

Accepted Answer

Mean, median, and mode are all approximately equal.

Question 7

Which of the following distributions is most likely to be skewed right (positively skewed)?

Accepted Answer

Distribution of house prices in a city.

Question 8

A frequency distribution table for continuous data has the following classes: 32-35, 36-39, 40-43, 44-47, 48-51. If the frequency for the class 36-39 is 9 and the total number of observations is 24, what is the relative frequency for this class?

Accepted Answer

$$ \frac{9}{24} = 0.375 $$

Question 9

Which of the following best describes a uniform distribution?

Accepted Answer

All classes have approximately equal frequencies.

Question 10

A stem-and-leaf plot is constructed for a data set. What is one advantage of a stem-and-leaf plot over a histogram?

Accepted Answer

It preserves the original data values.

Question 11

A histogram of exam scores is skewed left. Which of the following is most likely true?

Accepted Answer

The mean is less than the median.

Question 12

If a bar graph is constructed to display the frequency of injury locations, what must be true about the width of the bars?

Accepted Answer

All bars must have equal width.

Question 13

A dot plot is created for the number of televisions in 40 households. What type of data display is this, and what is one benefit?

Accepted Answer

Quantitative; it shows the distribution and individual data points.

Question 14

A frequency distribution for exit velocities of home runs uses a class width of 4 mph. If the lowest value is 94 mph, what is the lower limit of the second class?

Accepted Answer

$$ 94 + 4 = 98 $$

Question 15

Which of the following is NOT a step in constructing a frequency distribution for continuous data?

Accepted Answer

Listing each individual data value as a separate class.

Question 16

A survey asks people how many times they visited a doctor last year. Which type of data is this, and what is the best way to organize it?

Accepted Answer

Discrete quantitative; frequency distribution

Question 17

If the sum of the relative frequencies in a table is 0.98, what should you do?

Accepted Answer

Check for rounding errors and ensure the sum is 1.

Question 18

Which of the following best describes the difference between a bar graph and a histogram?

Accepted Answer

Bar graphs are for qualitative data; histograms are for quantitative data.

Question 19

A frequency distribution for the number of televisions in households shows that 10 out of 40 households have 3 televisions. What is the percentage of households with 3 televisions?

Accepted Answer

$$ \frac{10}{40} 	imes 100\% = 25\% $$

Descriptive Statistics: Organizing and Summarizing Data

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