Exam 4: Graphical Descriptive Techniques Numerical Data

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

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.

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.

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

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

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. Years Frequency 0 up to 5 12 5 up to 10 16 10 up to 15 42 15 up to 20 20 20 up to 25 10 Total 100

Which of the following is the sum of the relative frequencies for all classes? A The number of classes. B The class width. C The total number of observations in the data set. D One or 100 \%

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

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

The frequency distribution of the number of years of service for 100 employees is shown below. Years Frequency 0 up to 5 12 5 up to 10 16 10 up to 15 42 15 up to 20 20 20 up to 25 10 Total 100 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.

Which of the following is the most appropriate type of chart for determining the number of observations at or below a specific value? A A histogram. B A pie chart. C A time-series chart. D A cumulative frequency ogive.

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

Construct a stem-and-leaf display of the test grades for a university business statistics class, given below. 63 74 42 65 51 54 36 56 68 57 62 64 76 67 79 61 81 77 59 38 84 68 71 94 71 86 69 75 91 55 48 82 83 54 79 62 68 58 41 47

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

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.

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: Income 45 51 40 44 48 35 51 55 49 47 Rent 230 280 190 220 270 200 300 310 260 250 a. Draw a scatter diagram for these data with rent payment on the vertical axis. b. Describe the relationship between rent payment and income.

Consider the following cumulative frequency distribution. Class limits Cumulative frequency Up to 10 12 Up to 20 29 Up to 30 57 Up to 40 71 Up to 50 95 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.

The numbers of defective items produced by a machine over the last 25 days are as follows: 19 6 15 20 17 16 17 12 15 29 23 17 7 10 14 14 27 22 8 5 23 19 9 28 5 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?

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.

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