Question 1

Which of the following best describes the difference between descriptive statistics and inferential statistics?

Accepted Answer

Descriptive statistics summarize and organize data, while inferential statistics use a sample to make predictions or draw conclusions about a population.

Question 2

A researcher wants to estimate the average height of all 4th grade students in a city. She measures the height of 50 randomly selected students. What is the population in this study?

Accepted Answer

All 4th grade students in the city.

Question 3

Which of the following variables is best classified as qualitative (categorical) data?

Accepted Answer

Birth month as a name (e.g., 'January')

Question 4

Which of the following is an example of a discrete quantitative variable?

Accepted Answer

Number of bedrooms in a house

Question 5

A bar chart and a pie chart are both used to display which type of data?

Accepted Answer

Qualitative (categorical) data

Question 6

A frequency table shows the number of students earning each letter grade in a class. Why might a relative frequency table be more informative?

Accepted Answer

It relates the counts to the total number of students, allowing for easier comparison across different class sizes.

Question 7

Which of the following is a potential problem with the graph shown in the image of the trash cans labeled '1960' and '1980'?

Accepted Answer

The size of the trash cans is not proportional to the values, misleading the viewer.

Question 8

Suppose you are asked to organize the following data: the number of people who purchase concessions at a theater each night. Which graphical display would be most appropriate?

Accepted Answer

Stem-and-leaf diagram

Question 9

A histogram is different from a bar chart in that:

Accepted Answer

A histogram displays frequencies for classes of quantitative data, with bars touching to indicate continuous intervals.

Question 10

Which of the following best describes a positively skewed (right-skewed) distribution?

Accepted Answer

The mean is greater than the median.

Question 11

A sample of 10 students has the following test scores: 60, 62, 65, 67, 68, 70, 72, 75, 78, 80. What is the median score?

Accepted Answer

$$69$$

Question 12

Which formula correctly calculates the sample standard deviation $$s$$ for a data set $$x_1$$, $$x_2$$, ..., x_n$$ with sample mean $$\bar{x}$$?

Accepted Answer

$$s = \sqrt{\frac{\sum_{i=1}^n (x_i - \bar{x})^2$}{n-1}}$$

Question 13

A box plot is especially useful for:

Accepted Answer

Displaying the Five-Number Summary and identifying outliers

Question 14

Which sampling method is most likely to produce a representative sample of a population?

Accepted Answer

Simple random sampling

Question 15

A researcher wants to estimate the average income of all residents in a state. She divides the state into regions and randomly selects residents from each region in proportion to the region's population. What sampling method is she using?

Accepted Answer

Stratified sampling with proportional allocation

Question 16

If a data set has a mean of $$50$$ and a standard deviation of $$5$$, according to the Empirical Rule, approximately what percentage of data falls between $$40$$ and $$60$$?

Accepted Answer

$$68\%$$

Question 17

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Question 18

A 20% trimmed mean is calculated by:

Accepted Answer

Removing the lowest and highest 20% of values and calculating the mean of the remaining data

Question 19

Which of the following is an example of a misleading graph?

Accepted Answer

A bar chart with a truncated y-axis that exaggerates differences

Unit 1 Study Guide: Sampling Designs and Describing Data in Elementary Statistics

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