Question 1

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 the sizes of the intervals and determine the frequency within each interval. This allows for a clearer understanding of the distribution of the data.

Question 2

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 help show the strength of a linear relationship between two numerical variables, where a clear and tight line indicates a stronger linear relationship.

Question 3

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 is a correct definition of a symmetric histogram.

Question 4

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 5

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

Accepted Answer

This is true. An ogive is a graph that shows the cumulative frequency distribution of a set of data. It takes the form of a cumulative step plot, with the cumulative frequency plotted on the y-axis and the data values plotted on the x-axis.

Question 6

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 7

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

Time-series data refers to data collected over a period of time for a specific variable or set of variables, such as stock prices for a company over 30 trading days. Therefore, a list of share prices for an Australian company over 30 trading days would be an example of time-series data.

Question 8

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

Accepted Answer

The statement is true. A scatter diagram is a graph that displays the relationship between two variables. Each dot on the graph represents a single data point, with the position of the dot determined by the values of the two variables. The scatter diagram is a useful tool for identifying patterns in the relationship between the variables.

Question 9

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 10

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 11

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

Accepted Answer

This is a known property of relative frequency distributions. All the relative frequencies add up to 1 because they represent the proportions of the total frequency.

Question 12

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 suited for displaying the overall trend in a time-series, as it allows for the use of a continuous line that connects the data points over time. Bar charts are better for comparing discrete data points within a time-series.

Question 13

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

The stem is 4, and the leaves are 2, 5, and 6. Therefore, the three integers being described are 42, 45, and 46.

Question 14

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

Accepted Answer

A frequency distribution is a listing of the individual observations along with their corresponding frequencies, grouped into intervals or classes. It is not necessarily arranged in ascending or descending order.

Question 15

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. If most of the points fall relatively close to the line, it suggests that there is a strong linear relationship between the two variables.

Question 16

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

This is a correct statement. Historgrams represent numerical data while bar charts represent categorical data.

Question 17

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

Accepted Answer

The statement is true. The modal class is the class or classes with the highest frequency in a frequency distribution.

Question 18

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 19

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 the variables are not strongly related in a linear fashion. Without a clear linear pattern, it is difficult to predict future outcomes based on one variable's value alone.

Question 20

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

Accepted Answer

This statement is true. Time-series data is commonly depicted on line charts or bar charts as they allow for easy visualization of trends and patterns over time.

Quiz 4: Graphical Descriptive Techniques Numerical Data