Question 1

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 is used to represent numerical data and displays the frequency distribution of a continuous variable. On the other hand, a bar chart is used to represent categorical data, where each bar represents a different category or group. Therefore, the given statement is true.

Question 2

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

Accepted Answer

This is true, a scatter diagram is used to display the relationship between two numerical (quantitative) variables.

Question 3

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

Accepted Answer

When the points on a scatter diagram are widely dispersed and do not follow a clear pattern or line, it suggests that there is no linear relationship between the variables.

Question 4

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 5

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

Accepted Answer

In a relative frequency distribution, each frequency is divided by the total number of frequencies, so the sum of all these ratios (relative frequencies) will always be 1.

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

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, in case of multiple modes) is defined as the class(es) with the highest frequency. Therefore, the statement is true.

Question 8

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 9

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

Accepted Answer

Time-series data can be effectively represented using line charts or bar charts.

Question 10

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

Accepted Answer

This statement is true. An ogive is a graph of a cumulative frequency distribution.

Question 11

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 leaf values are 2, 5, and 6. Therefore, the numbers being described are 42, 45, and 46.

Question 12

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 statement is true. If most of the points in a scatter diagram fall close to a straight line, it suggests that there may be a linear relationship between the two variables being plotted. However, it is important to also consider other factors such as outliers and the strength of the relationship before making any conclusions.

Question 13

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

Accepted Answer

This is true. A frequency distribution is a table that shows how many times data appears within each class or category. It is used to summarize large sets of data and make it more manageable to analyze.

Question 14

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 overall trend because it shows a continuous line connecting the data points over time, whereas a bar chart shows individual values at each time point and may not depict the trend as clearly.

Question 15

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 the definition of a symmetric histogram.

Question 16

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 frequency of different values or groups of values in a dataset, not a listing of individual observations.

Question 17

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 18

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 a collection of observations made over time, such as daily share prices of a company.

Question 19

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 and direction of a linear relationship between two numerical variables. The closer the points on the graph form a straight line, the stronger the linear relationship is between the two variables.

Question 20

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

Accepted Answer

Class intervals of equal width allow for easy grouping of data and calculation of frequencies. It also helps in visualizing the distribution of data in a histogram or frequency polygon.

Quiz 4: Graphical Descriptive Techniques Numerical Data