Deck 4: Graphical Descriptive Techniques Numerical Data

Question 1

Which of the following statements best describes a stem-and-leaf display?

Answer 1

C

Question 2

Which of the following graphical display is can be used to describe relationship between two numerical (quantitative) variables?

Answer 2

A

Question 3

Which of the following is the best type of chart for illustrating the GDP of Australia from 1960 to 2010?

Answer 3

A

Question 4

Which of the following is the most important and commonly used graphical presentation of numerical (quantitative) data?

Question 5

A relative frequency distribution describes the number of data values that fall within each class, and may be presented in histogram form.

Question 6

Compared to the frequency distribution, the stem-and-leaf display provides more details, since it can describe the individual data values as well as show how many are in each group, or stem.

Question 7

A relative frequency distribution describes the proportion of data values that fall within each category.

Question 8

The stem-and-leaf display reveals far more information about individual values than does the histogram.

Question 9

Which of the following is the sum of the relative frequencies for all classes?

Question 10

Which of the following statements about histograms is true? $\begin{array}{|l|l|}\hline A&\text { A histogram shows the cumulative relative frequency distribution.}\\\hline B&\text { A histogram may be used as a graphical display of ordinal data.}\\\hline C&\text { A histogram may be used as a graphical display of categorical data.}\\\hline D&\text { A histogram generally has no gaps between rectangles, because it is a graphical display of}\\&\text {a numerical variable and the horizontal axis follows a number scale. }\\\hline \end{array}$

Question 11

Individual observations within each class may be found in a frequency distribution.

Question 12

Which of the following may be determined from the height of the bar in a relative frequency histogram?

Question 13

A cumulative frequency distribution lists the proportion of observations that are within or below each of the classes.

Question 14

Which of the following best describes the modal class?

Question 15

Which of the following statements is false? $\begin{array}{|l|l|}\hline A&\text {A frequency distribution counts the number of observations that fall into each of a series }\\&\text {of intervals, called classes that cover the complete range of observations.}\\\hline B&\text {The intervals in a frequency distributi on must not overlap to ensure that each observation }\\&\text {is assigned to an interval. }\\\hline C&\text {Although the frequency distribution provides information about how the numbers in the data }\\&\text { set are distributed, the information is more easily }\\&\text {understood and imparted by drawing a histogram. }\\\hline D&\text { The number of class intervals in a frequency distribution must be}\\&\text { the same as the number of observations.}\\\hline \end{array}$

Question 16

Which of the following statements is true? $\begin{array}{|l|l|}\hline A&\text {A histogram is created by drawing rectangles whose bases correspond to the class intervals, }\\&\text {and the area of each rectangle equals the total }\\&\text { number of observations in the sample.}\\\hline B&\text { A histogram can be used for only categorical variables.}\\\hline C&\text { A histogram is created by drawing rectangles whose bases correspond to the number }\\&\text { of observations in each class.}\\\hline D&\text { A histogram is created by drawing rectangles whose bases correspond to the class intervals, and the area}\\&\text { of each rectangle equals the number of observations in that class.}\\\hline \end{array}$

Question 17

Which of the following is the most appropriate type of chart for determining the number of observations at or below a specific value?

Question 18

When income increases, expenditure on imports tend to increase. Which of the following best describes this relationship?

Question 19

Which of the following best describes the shape of the distribution of incomes of all employees in large company?

Question 20

Which of the following statements is false? $\begin{array}{|l|l|}\hline A&\text { All calculations are permitted on numerical (quantitative) data}\\\hline B&\text {All calculations are permitted on nominal (categorical) data. }\\\hline C&\text {The most important aspect of ordinal data is the order of the data values.}\\\hline D&\text {The only permissible calculations on ordinal data are ones involving a ranking process. }\\\hline \end{array}$

Question 21

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.

Question 22

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

Question 23

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

Question 24

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

Question 25

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.

Question 26

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.

Question 27

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

Question 28

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.

Question 29

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.

Question 30

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.

Question 31

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

Question 32

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

Question 33

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

Question 34

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.

Question 35

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

Question 36

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

Question 37

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.

Question 38

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

Question 39

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.

Question 40

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

Question 41

Graphical excellence is displayed when a graph has a proper scale, the axis are marked correctly are the graph chosen appropriately tells the truth about the data.

Question 42

Construct a cumulative relative frequency distribution for the number of years of service for 100 employees, given the frequency distribution of the number of years of service for 100 employees is shown below.

Question 43

The frequency distribution of the number of years of service for 100 employees is shown below. a. Estimate the proportion of employees who have fewer than 10 years of service.
b. Estimate the proportion of employees who have more than 20 years of service.
c. Estimate the proportion of employees who have between 10 and 20 years of service.

Question 44

The following data are test grades for a university business statistics class. a. Construct a cumulative frequency distribution and a cumulative relative frequency distribution for the data.
b. What proportion of the grades is less than 60?
c. What proportion of the grades is more than 70?

Question 45

The ages of 25 salespersons in an organisation are given below. Construct an ogive for the data, and estimate the proportion of salespersons that are:
a. less than 30 years of age.
b. more than 40 years of age.
c. between 40 and 50 years of age.

Question 46

Construct a stem-and-leaf display of the test grades for a university business statistics class, given below.

Question 47

The relationship between expenditure on imports and household income may be described as a positive linear relationship.

Question 48

Describe briefly what the histogram and the stem-and-leaf displays tell you about the test grades for a university business statistics class.

Question 49

The numbers of defective items produced by a machine over the last 25 days are as follows:

a. Construct a frequency distribution and a relative frequency distribution for these data. Use five class intervals, with the lower boundary of the first class being five items.
b. Construct a relative frequency histogram for these data.
c. What is the relationship between the total area under the histogram you have constructed and the relative frequencies of observations?

Question 50

With a line graph, the horizontal axis is stretched out to get a deceptive steeper slope.

Question 51

If two numerical variables are linearly related, then it means that one variable is causing the other variable to react in a particular way.

Question 52

The weights in kilograms of a sample of 30 horses are given below:


a. Construct a cumulative relative frequency distribution for the data.
b. Construct an ogive for the data.
c. What proportion of horses weighs less than 160kgs?
d. What proportion of horses weighs between 145 and 165kgs?

Question 53

The table below shows the number of licensed hotels with at least 15 rooms in New South Wales from March 1998 to December 2009. a. Plot the time series.
b. When did the number of licensed hotels with at least 15 rooms in New South Wales grow fastest?

Question 54

Construct a relative frequency histogram for the test grades for a university business statistics class.

Question 55

Consider the following cumulative frequency distribution. Find the frequency for each of the following classes.
a. 0 up to 10.
b. 10 up to 20.
c. 20 up to 30.
d. 30 up to 40.
e. 40 up to 50.

Question 56

For a bar chart to show graphical excellence, the bars must be the same width irrespective of each bar's height.

Question 57

Construct an ogive for the test grades for a university business statistics class, and estimate the proportion of grades that are between 80 and 90.

Question 58

Construct a frequency distribution and relative frequency distribution for the test grades for a university business statistics class, data given in the following table. Use seven class intervals.

Question 59

Graphical deception is acceptable when the graph displays what the statistician would like the reader to believe, as opposed to the truth about the data.

Question 60

For each of the following numerical variables, describe if the distribution of data would be symmetrical, positively skewed or negatively skewed.
a. Annual incomes of employees in a multinational company.
b. Weights of 1kilogram labeled bags of flour, processed by a large manufacturing company.
c. Grades of students in an easy test.

Question 61

The bar chart below is of the colour of motor vehicles in a random sample. A student commented that the distribution was negatively skewed. Explain what is wrong with this statement.
Motor Vehicle Colour Relative Frequency Bar Chart

Question 62

The number of houses sold in a suburb in Sydney and the average monthly mortgage rates for 18 months randomly selected are shown in the following table. a. Draw a scatter diagram with the number of houses sold on the vertical axis.
b. Describe the relationship between mortgage rate and number of houses sold.

Question 63

The following table shows the annual incomes (in thousands of dollars) and weekly rent payments (dollars) of a sample of 10 individuals in country New South Wales:

a. Draw a scatter diagram for these data with rent payment on the vertical axis.
b. Describe the relationship between rent payment and income.

Question 64

The number of faulty items returned to a manufacturer of electric goods in the last 15 years is as follows: a. Construct a relative frequency bar chart for these data.
b. Construct a line chart.