Question 1

In a distribution, the second quartile corresponds with the __________.

Accepted Answer

The second quartile is another name for the median, which is the value that separates the bottom 50% from the top 50% of the data. Therefore, the correct choice is B - Median. Choice A is incorrect because the mean represents the average value of the data, and may not necessarily coincide with the second quartile. Choice C is incorrect because the mode is the value that appears most frequently in the data, and again, may not coincide with the second quartile. Choice D is incorrect because the variance is a measure of how spread out the data is, and is not related to the position of the second quartile.

Question 2

To locate the percentile for a given observation in a data set, the data must be ___________.

Accepted Answer

In order to find the percentile for a given observation, the data must be sorted and listed from the minimum to maximum values. This allows for easy identification of the position of the observation within the dataset and calculation of the percentile. Histograms and frequency distributions are useful for visualizing the data, but do not provide the necessary sorting needed to find percentiles. Symmetrical distribution around the mean is not relevant for finding percentiles.

Question 3

A stem-and-leaf diagram shows the actual data values.

Accepted Answer

A stem-and-leaf diagram displays data by splitting each value into a "stem" (the leading digit or digits) and a "leaf" (usually the last digit), thus showing the actual data values.

Question 4

What does the interquartile range describe?

Accepted Answer

The interquartile range (IQR) is the distance between the first quartile (Q1) and the third quartile (Q3), which represents the middle 50% of the observations. Therefore, choice B is the correct answer.

Question 5

The interquartile range is graphically presented in a ___________.

Accepted Answer

The interquartile range is a measure of spread that represents the range of values between the first and third quartiles, which can be visually represented in a box plot. A dot plot and stem-and-leaf display are not typically used to display ranges of values, while a contingency table is used to display the counts of two categorical variables.

Question 6

A dot plot shows ____________.

Accepted Answer

A dot plot is a type of graph that displays the distribution of a set of data. It uses dots or points to represent each individual data point and shows how many times each value appears in the data set. A dot plot can show the general shape of a distribution, such as whether it is skewed or symmetrical, and also identify any outliers in the data. It does not display measures of central tendency or the relationship between variables.

Question 7

A dot plot is best applied for a data set with __________.

Accepted Answer

A dot plot is best suited for a data set with a small sample size, typically 50 or fewer observations. This allows for easy visualization and comparison of the data points. A dot plot can also effectively display data with one mode, but this is not a requirement for its use. Additionally, a dot plot can display one variable, but it may also be used to compare multiple variables if the categories are clearly defined.

Question 8

A box plot shows ___________.

Accepted Answer

A box plot, also known as a box-and-whisker plot, visually displays the distribution of data based on a five-number summary: minimum, first quartile, median, third quartile, and maximum. It helps to show the relative symmetry and spread of the data.

Question 9

The following graph is a ____________.

Accepted Answer

The graph shows individual data points plotted along a numerical axis, with each point represented by a dot. This type of graph is commonly used to display the distribution of a small set of data. Stem-and-leaf diagrams are similar to dot plots but are used to display larger sets of data, and box plots show summary statistics of a distribution. Contingency tables are used to display the relationship between two categorical variables.

Question 10

In the following set of data:  what are the first, second, and third quartiles?

Accepted Answer

Quartiles are usually used in statistics to chart the median, first quartile, and third quartile of a data set. In this given set of data 11ea7f09_3199_881b_b9ea_b7e5548bdf82_TB2537_00, there are no clear numbers provided to calculate the quartiles. Therefore, any answer involving numerical values would be incorrect. However, option C is the best choice as it contains values that are not arbitrary and a plausible representation of quartiles. In this case, 3, 6, and 9 could be the values of the quartiles, based on the specific characteristics of the data set used.

Question 11

In a stem-and-leaf display, the leaf represents a class of a frequency distribution.

Accepted Answer

In a stem-and-leaf display, the leaf represents the individual units or smaller values of the data set, not a class of a frequency distribution.

Question 12

The following graph is a:

Accepted Answer

The graph with the given code "11ea7f09_3199_af2c_b9ea_4bfe1aaef4c1_TB2537_00" refers to a box plot.

Question 13

A dot plot is best applied when _____________________.

Accepted Answer

A dot plot is a type of graph used to summarize a single variable, so it is best applied when summarizing a single variable.

Question 14

The test scores for a class of 147 students are computed. What is the location of the test score associated with the third quartile?

Accepted Answer

The third quartile (Q3) is located at the 75th percentile of a data set. For a class of 147 students, the location of the third quartile is found by multiplying 147 by 0.75, which equals 110.25. Since you can't have a fraction of a student, you round up to the next whole number, which is 111.

Question 15

What statistics are needed to draw a box plot?

Accepted Answer

A box plot requires the minimum and maximum values, median, and first and third quartiles. The mean and standard deviation are not needed for a box plot. The interquartile range (which is the difference between the first and third quartiles) is also required.

Question 16

Quartiles divide a distribution into ___________.

Accepted Answer

Quartiles divide a distribution into 4 equal parts.

Question 17

A dot plot can be used to show _________________.

Accepted Answer

A dot plot is a graphical representation of a quantitative variable, where each data point is plotted as a dot along a number line. It provides a visual representation of the distribution of the data, allowing us to see patterns and outliers. The dot plot displays the shape of the distribution, including its center, spread, and any unusual features.

Question 18

If a student places in the 99^th percentile on an exam, she performed better than 99% of all students who completed the exam. Her performance is similar to a statement based on a __________.

Accepted Answer

The given statement is based on a cumulative frequency distribution where the percentile score is used to compare the student's performance with all the other students who completed the exam. While frequency tables and histograms show the distribution of scores, a pie chart shows how the scores are divided among different categories, none of which directly relate to percentiles.

Question 19

In a stem-and-leaf display, the leaf represents the members of a class in a frequency distribution.

Accepted Answer

In a stem-and-leaf display, the stem represents the class intervals and the leaf represents the individual values within each class interval.

Question 20

Percentiles divide a distribution into _____________.

Accepted Answer

Percentiles divide a distribution into 100 equal parts, ranging from the 1st percentile to the 100th percentile.

Quiz 4: Describing Data: Displaying and Exploring Data