Statistics Chapter 2
How do you find the class interval?
(Maximum value-minimum value)/k where k is the number of classes
How to set the individual class limits?
picking the starting point should (a)be rounded, (b) approximately half of excess of the cover should be tailed to the max and min values equally
A total of 1,000 residents in Minnesota were asked which season they preferred. One hundred liked winter best, 300 liked spring, 400 liked summer, and 200 liked fall. Develop a frequency table and a relative frequency table to summarize this information.
spring: 300 30% summer: 400 40% fall: 200 20% winter: 100 10%
What is class frequency?
Class frequency refers to the number of observations in each class
What is the most common graphics to present qualitative data?
1. A bar chart 2. Pie chart
What three graphical methods help display a frequency distribution?
1. Histogram 2. Frequency polygon 3. Cumulative frequency polygon
What are the steps to create a frequency distribution?
1. decide on the number of classes 2. determine the class interval 3. set the individual class limits
How to decide on the number of classes?
2 to the k rule When 2 raised to the power of k is greater than the number of observations, k is the ideal number of classes.
A set of data consists of 38 observations. How many classes would you recommend for the frequency distribution?
25 = 32, 26 = 64, therefore, 6 classes
A pie chart shows the relative market share of cola products. The "slice" for Pepsi- Cola has a central angle of 90 degrees. What is its market share?
25%
"2 to the k rule" formula
2^k>n
In a marketing study, 100 consumers were asked to select the best digital music player from the iPod Touch, Sony Walkman, and Zune HD. To summarize the consumer responses with a frequency table, how many classes would the frequency table have?
3
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?
6 classes 40
A set of data consists of 45 observations between $0 and $29. What size would you recommend for the class interval?
6 classes class interval=5
A set of data consists of 230 observations between $235 and $567. What class interval would you recommend?
8 classes class interval 45/50
What is a pie chart?
A chart that shows the proportion or percentage that each class represents of the total number of frequencies.
What is a 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.
What is a 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.
What is a frequency table?
A grouping of qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.
What is a frequency distribution?
A grouping of quantitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.
Two thousand frequent business travellers were asked which Midwestern city they prefer: Indianapolis, Saint Louis, Chicago, or Milwaukee. One hundred liked Indianapolis best, 450 liked Saint Louis, 1,300 liked Chicago, and the remainder preferred Milwaukee. Develop a frequency table and a relative frequency table to summarize this information.
Indianapolis: 100 5% Saint Louis: 450 22.5% Chicago: 1300 65% Milwaukee: 150 7.5%
What is a frequency polygon?
It's a graphical representation of data that displays data in a line graph form.
What type of data is a histogram used for?
Quantitative data
What is relative class frequency?
The "relative frequency" of each class is the proportion of the data that falls in that class. Class frequencies shows the fraction of the total number of observations in each class.
How to determine the class interval?
The classes all taken together should cover at least the distance from the minimum value to the maximum value of the data. i=class interval k=number of classes "i" is greater than (max-min)/k
what is raw data/ungrouped data?
Unorganized information
What is relative frequency distribution?
a grouped frequency distribution which shows the percentage of all the elements that fall within each class interval
What is mutually exclusive classes?
a particular observation can be assigned to only one class
Wachesaw Manufacturing Inc. produced the following number of units in the last 16 days. 27 26 27 28 27 26 28 28 27 31 25 30 25 26 28 26 The information is to be organized into a frequency distribution. a. How many classes would you recommend? b. What class interval would you suggest? c. What lower limit would you recommend for the first class? d. Organize the information into a frequency distribution and determine the relative frequency distribution. e. Comment on the shape of the distribution.
a. 24 = 16, suggests 5 classes b. i ≥ 31 − 25 5 = 1.2 Use interval of 1.5. c. 24 e. The largest concentration is in the 27.0 up to 28.5 class (8).
Barry Bonds of the San Francisco Giants established a new single-season Major League Baseball home run record by hitting 73 home runs during the 2001 season. This record still stands today. Listed below is the sorted distance of each of the 73 home runs. 320 370 380 405 410 420 430 450 320 375 390 410 410 420 430 480 347 375 390 410 411 420 435 488 350 375 391 410 415 420 435 360 375 394 410 415 420 436 360 380 396 410 416 420 440 360 380 400 410 417 429 440 361 380 400 410 417 430 440 365 380 400 410 420 430 440 370 380 400 410 420 430 440 (a) For these data, show that seven classes would be used to create a frequency distribution using the 2k rule. (b) Show that a class interval of 30 would summarize the data in seven classes. (c) Construct frequency and relative frequency distributions for the data with seven classes and a class interval of 30. Start the first class with a lower limit of 300. (d) How many home runs traveled a distance of 360 up to 390 feet? (e) What percentage of the home runs traveled a distance of 360 up to 390 feet? (f) What percentage of the home runs traveled a distance of 390 feet or more?
a. 26 = 64 < 73 < 128 = 27, so seven classes are recommended. b. The interval width should be at least (488 − 320)/7 = 24. Class intervals of either 25 or 30 are reasonable. c. Assuming a class interval of 25 and beginning with a lower limit of 300, eight classes are required. If we use an interval of 30 and begin with a lower limit of 300, only seven classes are required. Seven classes is the better alternative. d. 17 e. 23.3%, found by 17/73 f. 71.2%, found by (27 + 22 + 1 + 2)/73
What should you do to avoid unclear or overlapping classes?
make the classes "up to "
In the first quarter of last year, the 11 members of the sales staff at Master Chemical Company earned the following commissions: $1,650 $1,475 $1,510 $1,670 $1,595 $1,760 $1,540 $1,495 $1,590 $1,625 $1,510 (a) What are the values such as $1,650 and $1,475 called? (b) Using $1,400 up to $1,500 as the first class, $1,500 up to $1,600 as the second class, and so forth, organize the quarterly commissions into a frequency distribution. (c) What are the numbers in the right column of your frequency distribution called? (d) Using the frequency distribution of quarterly commissions: What is the class with the highest frequency of earned commissions? What is the smallest commission? What is the largest commission? What is the typical earned commission?
a. The raw data or ungrouped data c. Class frequencies. d. The largest concentration of commissions is $1,500 up to $1,600. The smallest commission is about $1,400 and the largest is about $1,800. The typical amount earned is $1,550.
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? b. Draw a bar chart for the table. c. Draw a pie chart. d. If Wellstone Inc. plans to produce 1 million cell phone covers, how many of each color should it produce?
a. frequency table b. c. d. bright white 0.1 m metallic black 0.08 m magnetic lime 0.25 m tangerine orange 0.35 m fusion red 0.22 m
DeCenzo Specialty Food and Beverage Company has been serving a cola drink with an additional flavoring, Cola-Plus, that is very popular among its customers. The company is interested in customer preferences for Cola-Plus versus Coca-Cola, Pepsi, and a lemon-lime beverage. They ask 100 randomly sampled customers to take a taste test and select the beverage they prefer most. The results are shown in the following table: Cola-Plus 40 Coca-Cola 25 Pepsi 20 Lemon-Lime 15 (a) Are the data qualitative or quantitative? Why? (b) What is the table called? What does it show?
a. qualitative b. frequency table
The manager of the BiLo Supermarket in Mt. Pleasant, Rhode Island, gathered the following information on the number of times a customer visits the store during a month. The responses of 51 customers were: 5 1 8 1 3 14 4 10 3 1 7 8 1 2 6 9 4 4 5 2 4 4 9 12 5 4 11 6 5 3 4 6 12 2 3 4 6 5 7 6 3 6 6 4 5 7 5 15 1 6 1 a. Starting with 0 as the lower limit of the first class and using a class interval of 3, organize the data into a frequency distribution. b. Describe the distribution. Where do the data tend to cluster? c. Convert the distribution to a relative frequency distribution.
b. The largest group of shoppers (21) shop at the BiLo Supermarket 3, 4, or 5 times during a one-month period. Some customers visit the store only 1 time during the month, but others shop as many as 15 times. c. Number of Percent Visits of Total 0 up to 3 17.65 3 up to 6 41.18 6 up to 9 25.49 9 up to 12 7.84 12 up to 15 5.88 15 up to 18 1.96 Total 100.00
The number of observations in each class is called the ....
class frequency
How is collectively exhaustive?
every observation is included, without any missing one.
