Question 1

A histogram is said to be symmetric if, when we draw a vertical line down the center of the histogram, the two sides are mirror images of each other.

Accepted Answer

This statement correctly defines what it means for a histogram to be symmetric.

Question 2

Frequency polygons are useful for obtaining a general idea of the shape of the distribution, because they are a bar chart.

Accepted Answer

Frequency polygons are useful for obtaining a general idea of the shape of the distribution, but they are not a bar chart; they are a graphical tool that uses lines to connect the midpoints of each interval, or class, to show the distribution of data.

Question 3

The modal class (classes) of a frequency distribution is the class (are the classes) with the highest frequency.

Accepted Answer

The modal class (or classes, if there is a tie) is defined as the class(es) with the highest frequency in a frequency distribution.

Question 4

In any relative frequency distribution, the sum of all the relative frequencies is always equal to 1.

Accepted Answer

This is true by definition of a relative frequency distribution. The relative frequency of each value represents the proportion of the total frequency accounted for by that value, so it follows that the sum of all the relative frequencies will equal 1 (or 100% if expressed as a percentage).

Question 5

When choosing between a line chart and a bar chart to display a time-series of data, if the main objective is to display the overall general movement, or trend, in the time-series, a line chart is best.

Accepted Answer

A line chart is best for displaying the overall trend in a time-series of data, as it shows the continuous flow of the data points over time. A bar chart may be better suited for comparing discrete values at different points in time.

Question 6

The lowest value in a set of data is 140, and the largest value is 270. If the resulting frequency distribution is to have ten classes of equal width, the common class width will be 27.

Accepted Answer

The class width is calculated by subtracting the lowest value from the highest value and then dividing by the number of classes. So, (270 - 140) / 10 = 13.

Question 7

A scatter diagram which has points widely dispersed, where no clear line is visible, indicates no linear relationship between the variables.

Accepted Answer

A scatter diagram with widely dispersed points indicates that there is no clear pattern or relationship between the variables. This means that there is no linear relationship between them, as a linear relationship would be indicated by the points forming a line.

Question 8

If we draw a straight line through the points in a scatter diagram and most of the points fall relatively close to the line, we say that there is a linear relationship between the two variables.

Accepted Answer

This is the definition of a linear relationship in a scatter diagram.

Question 9

The difference between a histogram and a bar chart is that the histogram represents numerical (quantitative) data while the bar chart represents nominal (categorical) data.

Accepted Answer

A histogram displays the distribution of numerical data while a bar chart displays the frequency or count of categorical data.

Question 10

A stem-and-leaf display describes two-digit integers between 20 and 70. For one of the classes displayed, the row appears as 4 | 2 5 6. The numerical values being described are 42, 45 and 46.

Accepted Answer

In a stem-and-leaf display, the first digit(s) represent the stem and the last digit represents the leaf. Therefore, in the row 4 | 2 5 6, the stem is 4 and the leaf values are 2, 5, and 6. Combining the stem and leaf values gives us the integers 42, 45, and 46.

Question 11

A frequency distribution shows the number of data values falling within each class.

Accepted Answer

A frequency distribution displays the number of data values that fall within each class or interval.

Question 12

Class intervals of equal width make the interpretation of a frequency distribution easier.

Accepted Answer

Class intervals of equal width make it easier to compare and group data, as all intervals have the same range. This allows for a clearer representation of the distribution of the data.

Question 13

A list of share prices of 20 Australian companies at the end of a trading day would be an example of time-series data.

Accepted Answer

This list represents cross-sectional data because it captures a snapshot of share prices at a single point in time, rather than tracking the changes in share prices over a period of time.

Question 14

The strength of a linear relationship between two numerical variables may be illustrated by a line graph, where the closer the points form a line, the stronger the linear relationship between the two variables.

Accepted Answer

This statement is true. A line graph can visually demonstrate the strength of a linear relationship between two numerical variables, and when the points form a line, it indicates a strong linear relationship.

Question 15

The graphical format used to display the relationship between two numerical (quantitative) variables is the scatter diagram.

Accepted Answer

This statement is true. The scatter diagram is a visual representation of the relationship between two numerical variables, often used in data analysis and statistical studies. It displays data points on a coordinate plane with one variable represented on the x-axis and the other variable represented on the y-axis. The pattern of points can give insight into whether there is a relationship, and what type of relationship it is, between the two variables.

Question 16

A cumulative frequency distribution presented in graphical form is called an ogive.

Accepted Answer

An ogive is a graph that shows the cumulative frequency distribution.

Question 17

A skewed histogram is one with a long tail extending either to the right or left. The former is called negatively skewed, and the latter is called positively skewed.

Accepted Answer

A skewed histogram with a long tail extending to the right is called positively skewed, and one with a long tail extending to the left is called negatively skewed.

Question 18

A frequency distribution is a listing of the individual observations arranged in ascending or descending order.

Accepted Answer

A frequency distribution is a table or graph that summarizes the distribution of a set of data, displaying the frequency or proportion of each value or range of values of a variable. It does not list individual observations.

Question 19

A list of share prices of one Australian company, at the end of a trading day for the period of 30 trading days, would be an example of time-series data.

Accepted Answer

A list of share prices over a period of 30 trading days represents a set of data collected over time, which is a characteristic of time-series data.

Question 20

Time-series data may be graphically depicted on a line chart or a bar chart.

Accepted Answer

Time-series data is commonly displayed on line charts and bar charts to visualize changes over time. A line chart is best suited for continuous data, while a bar chart is useful for comparing discrete values at certain points in time.

Quiz 4: Graphical Descriptive Techniques Numerical Data