Statistics MH Chapter 2 HW

Two thousand six hundred frequent business travelers were asked which Midwestern city they prefer: Indianapolis, Saint Louis, Chicago, or Milwaukee. One hundred and thirteen liked Indianapolis best, 455 liked Saint Louis, 1,395 liked Chicago, and the remainder preferred Milwaukee. Prepare a frequency table and a relative frequency table to summarize this information. (Round "Relative Frequency" answers to 3 decimal places.)

Explanation City Freq. Rel. Freq. Found by Indianapolis 113 0.043 113 / 2,600 St. Louis 455 0.175 455 / 2,600 Chicago 1,395 0.537 1,395 / 2,600 Milwaukee 637 0.245 637 / 2,600 Total 2,600 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.

The following is the number of minutes to commute from home to work for a group of 25 automobile executives. 34 49 34 36 44 54 44 50 46 43 34 43 31 45 39 34 47 44 25 38 54 53 47 37 40 How many classes would you recommend? Number of classes What class interval would you suggest? (Round up your answer to the next whole number.) Class interval Organize the data and plot a frequency distribution on a piece of paper. Comment on the shape of the frequency distribution.

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. So 5 classes are recommended because 24 = 16 < 25 and 25 = 32 > 25. b. i ≥54 − 25= 5.8 suggests an interval of 6.5 c. It is fairly symmetric, with most of the values between 43 and 48.

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 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.

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: a. What kind of variable is delivery performance? What scale is used to measure delivery performance? b. Construct a frequency table for delivery performance for last month. c. Construct a relative frequency table for delivery performance last month. (Round your answers to 2 decimal places.) d.

a. Variable - Qualitative Scale - non-numeric b. Performance Frequency Early 23 On-time 68 Late 8 Lost 1 c. Performance Relative Frequency Early 0.23 On-time 0.68 Late 0.08 Lost 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.

The number of families who used the Minneapolis YWCA day care service was recorded over a 30-day period. The results are as follows: 32 66 62 68 68 33 54 34 42 41 17 39 23 44 44 24 37 49 54 17 58 62 50 46 63 59 52 54 58 12 Construct a cumulative frequency distribution of this data. (Round your calculated class interval up to the nearest multiple of 5.)

Class Cumulative Frequency 0 up to 15 1 15 up to 30 5 30 up to 45 14 45 up to 60 24 60 up to 75 30 Explanation 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. Thus 5 classes are recommended because 2^4 = 16 <30 < 32 = 2^5. The classes must cover at least the distance from the lowest value (12) in the data up to the highest value (68). The class interval is at least 11.2, found by (68 - 12)/5. Use 15 for convenience. Compute cumulative frequencies by adding successive class frequencies starting from the lowest or first class value.

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 6 5 6 up to 12 12 12 up to 18 25 18 up to 24 8 24 up to 30 2 Total 52

How many employees were studied? Number of employees 52 What is the midpoint of the first class? (Round your answer to 1 decimal place.) Midpoint 3.0 unit A frequency polygon is to be drawn. What are the coordinates of the plot for the third class? (Round your answer to 1 decimal place.) x =15.0, y =25 Explanation b.3.0 thousand miles, computed by adding the limits of 0 and 6 then dividing the result by 2. d.x = 15.0 (the class midpoint), y = 25 (the number of employees in that class)

Molly's Candle Shop has several retail stores in the coastal areas of North and South Carolina. Many of Molly's customers ask her to ship their purchases. The following chart shows the number of packages shipped per day for the last 100 days. For example, the first class shows that there were 5 days when the number of packages shipped was 0 up to 5.

What is this chart called? Histogram What is the total number of packages shipped? Frequency 100 What is the class interval? Class Interval 5 What is the class frequency of the 25 up to 30 class? Class frequency 10 What is the relative frequency of the 25 up to 30 class? (Round your answer to 2 decimal places.) Relative frequency 0.10 What is the midpoint of the 25 up to 30 class? (Round your answer to 1 decimal place.) Midpoint 27.5 On how many days were there 15 or more packages shipped? Number of days 54 Explanation a.A histogram is 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. b.100, found by summing the individual class frequencies 5 + 13 + 28 + 23 + 18 + 10 + 3. c.5, found by subtracting the lower limit of a class from the lower limit of the next class. d.There are 10 values between 25 and 30. e.0.10, found by dividing the class frequency (10) by the total of all the frequencies (100). f.The class midpoint is computed by adding the lower limits of consecutive classes and dividing the result by 2. In this case (25 + 30)/2 is equal to 27.5. g.54, found by adding the class frequencies 23 + 18 + 10 + 4.