Chapter 2 - Describing Data

Which of the following graphs are used to summarize quantitative data?

- Frequency polygon - Histogram Not: - Bar chart - Frequency table

Suppose a frequency distribution has the following consecutive classes: $20 up to $30 $30 up to $40 $40 up to $50 What is the class midpoint for the first class?

$25

Which of the following are true regarding the class midpoint?

- It is halfway between the lower limits of two consecutive classes. - It best represents the values in a class. - It is halfway between the upper limits of two consecutive classes. Not: - The average value of the observations in a class interval. - It is halfway between the highest and lowest classes. Explanation: Class midpoint refers to a single class.

Which two of the following practices is commonly used in setting class limits for a frequency distribution?

- Placing "excess" interval width equally in the two tails of the distribution. - Rounding the class interval up. Not: - Deleting data which is too low or too high to fit convenient intervals. - Overlapping the upper limit with the lower limit of the next higher class.

Which of the following are characteristics of bar charts?

- Bar charts are used for qualitative data - Plotted rectangles should be the same width. - There should be gaps between bars. Not: - Plotted rectangles should be the same height.

To divide data with the high value of H and a low value L into k classes, the class interval must be:

- at least (H-L)/k Not: - one fifth of the range - at most (H-L)/k - equal to (H-L)/k Explanation: In most instances, this value will be fractional and the number of classes should be an integer. When this calculation results in an integer, the limit must be increased to include all observations.

The value shown on the vertical axis of a cumulative frequency polygon for a particular class is found by:

- counting the number of observations less than the upper limit of the class Not: - counting the number of observations within the class Explanation: this is the frequency of the class

A cumulative frequency distribution:

- shows the number of observations less than each class upper limit Not: - shows the number of observations within each class - Plots a point each (class midpoint, frequency)

Relative frequencies are:

- the fraction or percentage of observations in each class interval Not: - the number of observations of a particular value in a set of data - the number of observation in each class interval

Place the following steps used in constructing a frequency distribution into correct order.

1. Decide on the number of classes 2. Determine class width. 3. Set individual class limits. 4. Tally the number of observations in each class.

Suppose you are trying to summarize a data set a maximum value of 70 and a minimum value of 1. If you have decided to use 7 classes, which one of the following would be a reasonable class interval?

10

Frequency distribution

A grouping of quantitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.

In the cumulative frequency polygon shown, about how many observations are there between a value of 200 and 250?

50 Explanation: You must subtract the observations for 200 from the observations for 250.

A business statistics instructor teaches a class with 83 students. Suppose he would like to create a frequency distribution to summarize their 83 final exam scores. Using the 2^k rule, how many classes should be used?

7

Pie Chart

A chart that shows the proportion or percentage that each class represents of the total number of frequencies.

Histogram

A graph in which the classes are marked on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are represented by the heights of the bars, and the bars are drawn adjacent to each other.

Bar Chart

A graph that shows qualitative classes on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are proportional to the heights of the bars.

Frequency Table

A grouping of qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.

Two thousand seven hundred frequent business travelers were asked which Midwestern city they prefer: Indianapolis, Saint Louis, Chicago, or Milwaukee. One hundred and twenty five liked Indianapolis best, 454 liked Saint Louis, 1,215 liked Chicago, and the remainder preferred Milwaukee. Prepare a frequency table and a relative frequency table to summarize this information.

City: Frequency: Relative Frequency: 1. Indianapolis - 125 - 0.046 2. St. Louis - 454 - 0.168 3. Chicago - 1,215 - 0.450 4. Milwaukee - 906 - 0.336 Explanation: Relative Frequency found by: 1. 125 / 2,700 2. 454 / 2,700 3. 1,215 / 2,700 4. 906 / 2,700 Do not multiply by 100. A frequency table groups qualitative data into mutually exclusive classes showing the number of observations in each class. In this case the classes are the cities and the number of observations is the number of travelers preferring each city. Each of the class frequencies is divided by the total number of observations to compute the relative frequency.

A frequency polygon shows the shape of a distribution and is similar to:

a histogram Not: - frequency table - pie chart - bar chart

frequency polygon

also shows the shape of a distribution and is similar to a histogram. graph of a frequency distribution that shows the number of instances of obtained scores, usually with the data points connect by straight lines

Suppose a cumulative frequency distribution is used to summarize n observations. The cumulative frequency for the last class will always be:

equal to n.

The number of observations in each class is called the class ___________.

frequency

Regarding frequency tables and frequency distributions, which one of the following is true?

- Both use mutually exclusive classes. Not - Only frequency distributions use qualitative data. - Frequency distributions show percentages and frequency tables don't.

Which of the following would be a use of a frequency table?

- Gender of students in a business statistics course. - State of residence of students in a business statistics course. - Majors of students in a business statistics course. Not: - Age of students in a business statistics course.

Which of the following features is an advantage that the frequency polygon has over the histogram?

- It can directly compare two or more frequency distributions Not: - The frequency polygon shows relative frequencies with respect to a circle, not bars. - It depicts each class as a rectangle, with the height representing the number of observations.

Which of the following can be observed from a histogram?

- The approximate number of observations. - The spread of the data - The concentration of the data - The shape of the distribution Not: - The relationship between two variables.

Which one of the following is true about pie charts?

- The area of a slice for a class relative to the whole pie should match its relative frequency.

Identify whether the table given below is a frequency table or a frequency distribution. Number of spots purchased: Frequency: 80 up to 90 - 2 90 up to 100 - 7 100 up to 110 - 6 110 up to 120 - 9 120 up to 130 - 8

Frequency distribution Not: Frequency table Explanation A frequency table groups qualitative data into mutually exclusive classes showing the number of observations in each class. On the other hand, a frequency distribution involves quantitative data.

Determining class interval formula

Maximum Value - Minimum Value / K Example: For the Applewood Auto Group, the min value is $294 and the max value is $3,292. If we need 8 classes, the interval should be: $3,292 - $294 / 8 = $374.75 - Round to nearest multiple of 10 or 100

Which of the following features is not part of a histogram?

The frequency of occurrence of a nominal variable. Explanation: Histograms are used to display properties of quantitative variables. (interval or ratio level) Not not: - Quantitative data divided into classes. - Adjacent bars whose height represents a number or a fraction. - The frequency of occurrence of data within classes.

Which of the following is true regarding raw data?

- Raw data is simply a listing of data before summarizing it. Not: - Raw data is the tally of data in each class - Raw data refers to the form of the data after grouping has taken place. - Raw data is the result of dividing frequencies by the total number of observations.

The following cumulative frequency polygon shows the hourly wages of a sample of certified welders in the Atlanta, Georgia, area. A. How many welders were studied? B. What is the class interval? C. About how many welders earn less than $15 per hour? D. About 50% of the welders make less than what amount? E. Twenty of the welders studied made less than what amount? F. About what percent of the welders make less than $15 per hour? ------ come back to hmk for chart ------ chegg --------

A. 50, because the vertical axis on the left ends at 50. B. 5, found by subtracting the lower limit of a class from the lower limit of the next class. C. 30, found by starting at $15 on the horizontal axis, up to the polygon and then across to the vertical axis on the left. D. About $14 per hour, found by starting at 50 percent on the vertical axis on the right, over to the polygon and then down to the horizontal axis. E. About $11 per hour, found by starting at 20 on the vertical axis on the left, over to the polygon and then down to the horizontal axis. F. About 60%, found by starting at $15 on the horizontal axis, up to the polygon and then across to the vertical axis on the right.

.Wellstone Inc. produces and markets replacement covers for cell phones in five different colors: bright white, metallic black, magnetic lime, tangerine orange, and fusion red. To estimate the demand for each color, the company set up a kiosk in the Mall of America for several hours and asked randomly selected people which cover color was their favorite. The results follow: Bright white 130 Metallic black 104 Magnetic lime 325 Tangerine orange 455 Fusion red 286 A. What is the table called? The table is called a ________ table. B. If Wellstone Inc. plans to produce 1 million cell phone covers, how many of each color should it produce? 1. Bright white: 2. Metallic black: 3. Magnetic lime: 4. Tangerine orange: 5. Fusion red:

A. frequency B. 1. 100,000 2. 80,000 3. 250,000 4. 350,000 5. 220,000 A. This is a frequency table because it groups qualitative data into mutually exclusive classes showing the number of observations in each class. B. The relative frequencies are 0.1 for white, 0.08 for black, 0.25 for lime, 0.35 for orange, and 0.22 for red. The number needed to produce is found by multiplying the relative frequency by 1,000,000. These are 100,000 white, 80,000 black, 250,000 lime, 350,000 orange, and 220,000 red.

The following frequency distribution reports the number of frequent flier miles, reported in thousands, for employees of Brumley Statistical Consulting Inc. during the most recent quarter. Frequent Flier Miles (000) Number of Employees 0 up to 3 - 5 3 up to 6 - 12 6 up to 9 - 23 9 up to 12 - 8 12 up to 15 - 2 Total 50 A. How many employees were studied? B. What is the midpoint of the first class? C. A frequency polygon is to be drawn. What are the coordinates of the plot for the first class?

A. Number of employees: 50 B. Midpoint: 1.5 C. X = 1.5 Y = 5 Explanation: B. 1.5 thousand miles, computed by adding the limits of 0 and 3 then dividing the result by 2. C. x = 1.5 (the class midpoint), y = 5 (the number of employees in that class)

Speedy Swift is a package delivery service that serves the greater Atlanta, Georgia, metropolitan area. To maintain customer loyalty, one of Speedy Swift's performance objectives is on-time delivery. To monitor its performance, each delivery is measured on the following scale: early (package delivered before the promised time), on-time (package delivered within 15 minutes of the promised time), late (package delivered more than 15 minutes past the promised time), or lost (package never delivered). Speedy Swift's objective is to deliver 99% of all packages either early or on-time. Speedy collected the following data for last month's performance: On-time On-time Early Late On-time On-time On-time On-time Late On-time Early On-time On-time Early On-time On-time On-time On-time On-time On-time Early On-time Early On-time On-time On-time Early On-time On-time On-time Early On-time On-time On-time Early Early On-time On-time On-time On-time On-time Late Late On-time On-time On-time On-time On-time On-time On-time On-time Late Early On-time Early On-time Lost On-time On-time On-time Early Early On-time On-time Late Early On-time On-time On-time On-time On-time On-time Early On-time Early On-time Early On-time Late On-time On-time Early On-time On-time On-time Late On-time On-time On-time On-time On-time On-time On-time On-time On-time Early Early On-time On-time On-time A. What kind of variable is delivery performance? What scale is used to measure delivery performance? 1. Variable: ? 2. Scale: ? B. Construct a frequency table for delivery performance for last month. Performance: Frequency: ? 1. Early 2. On-time 3. Late 4. Lost C. Construct a relative frequency table for delivery performance last month. Performance: Relative Frequency: ? 1. Early 2. On-time 3. Late 4. Lost

A. 1. Qualitative 2. Ordinal B. 1. 20 2. 71 3. 8 4. 1 C. 1. 0.2 2. 0.71 3. 0.08 4. 0.01 Explanation: a.There is an order to the scale. "Early" is faster than "on-time", which is faster than "late", which is faster than "lost". So the scale is ordinal. The performance is non-numeric. So the variable is qualitative. b.A frequency table groups qualitative data into mutually exclusive classes showing the number of observations in each class. c.Relative frequencies are computed by dividing each class frequency by the total of all observations.

A set of data contains 53 observations. The minimum value is 42 and the maximum value is 129. The data are to be organized into a frequency distribution. A. How many classes would you suggest? B. What would you suggest as the lower limit of the first class?

A. Classes: 6 B. Lower limit: 15 Explanation: A. For the number of classes (k) select the smallest integer such that 2 to the power of k is greater than the number of observations. 25 = 32, 26 = 64 suggests 6 classes. B. The classes must cover at least the distance from the lowest value (42) in the data up to the highest value (129). So the class interval (i) is at least i≥129−426=14.5 . It is more convenient to round up to an interval of 15. Start first class a little below the lowest value in the data of 42. Forty is a good value. Note that the last class will have an upper limit of 130. Therefore, all the values will be included in the frequency distribution.

Which of the following operations is true regarding relative frequency distributions?

The relative frequency is found by dividing the class frequencies by the total number of observations. Not: - The sum of the relative frequencies is equal to the number of observations. - No two classes can have the same relative frequencies. - The sum of the relative frequencies must be less than 1.