////
The same frequency distribution table can be obtained by using MINITAB as follows:
MINITAB
1 Enter the data in column C1.
2 From the Menu bar select Data Recode To Text. This prompts the following dialog box to appear on the screen.
3 Enter C1 in the box under Recode values in the following columns.
4 Select Recode ranges of values from the pulldown menu next to Method.
5 Enter Lower and Upper endpoints as needed and make sure to change the final upper endpoint to 152.1. Type Recoded values in the interval format as previously shown.
6 Select Lower endpoint only from the pulldown menu next to Endpoints to include. Then, for the Storage location for the recoded columns, select At the end of the current worksheet from the pulldown menu.
7 Now from the Menu bar select Stat Tables Tally Individual Variables. This prompts the following dialog box to appear on the screen:
8 In this dialog box, enter C2 Recoded Data in the box under variables.
9 Check all the boxes under Display and click OK. The frequency distribution table as shown below will appear in the Session window
This frequency distribution table also can be obtained by using R as follows:
USING R
First, we define the required classes using the built in ‘seq()’ function. Then, we use the ‘cut()’ function to assign a corresponding class to each observation. As explained in Example 2.3.2, we then use the ‘table()’ function on class variable and the ‘cusum()’ function on the frequency results. The task can be completed by running the following R code in the R Console window.
#Assign given data to the variable RodData RodData = c(145,140,120,110,135,150,130,132,137,115,142,115,130, 124,139,133,118,127,144,143,131,120,117,129,148,130,121,136,133, 147,147,128,142,147,152,122,120,145,126,151) #To define the intervals breaks = seq(110, 152, by=7) #To assign each observation to its interval RodData.split = cut(RodData, breaks, right=FALSE) #To obtain the frequency of data in each class RodData.freq = table(RodData.split) #To combine necessary columns freq.dist = cbind(RodData.freq,100*RodData.freq/sum(RodData.freq), cumsum(RodData.freq), 100*cumsum(RodData.freq)/sum(RodData.freq)) #To name the table columns colnames(freq.dist) = c(‘Frequency’,‘Percentage’, ‘Cum.Frequency’,‘Cum.Percentage’) freq.dist #R output
| Frequency | Percentage | Cum.Frequency | Cum.Percentage | |
|
|
3.00 | 7.69 | 3.00 | 7.69 |
|
|
7.00 | 17.95 | 10.00 | 25.64 |
|
|
8.00 | 20.51 | 18.00 | 46.15 |
|
|
7.00 | 17.95 | 25.00 | 64.10 |
|
|
6.00 | 15.38 | 31.00 | 79.49 |
|
|
8.00 | 20.51 | 39.00 | 100.00 |
PRACTICE PROBLEMS FOR SECTION 2.3
1 The following data give the results of a customer sample survey for product satisfaction conducted by a manufacturing company. The numbers 1, 2, 3, 4, and 5 represent the satisfaction levels: very satisfied, fairly satisfied, neutral, fairly unsatisfied, and very unsatisfied, respectively.11334243151224112442542213445523232324431515411152Prepare a frequency distribution table.Determine the percentages for all categories.What percentage of the customers in this sample survey was very satisfied or fairly satisfied?
2 An engineering school arranged a charity concert to raise funds for Iraq war veterans. The following data give the status of 40 randomly selected students who attended the concert. The numbers 1, 2, 3, and 4 represent the categories freshman, sophomore, junior, and senior, respectively.2341121132133444113233333433342322314223Prepare a frequency distribution table.Determine the percentages for all categories.What percentage of the students in this sample survey were juniors or seniors?
3 The following data give the responses of 36 senior citizens who were asked about the engine size of their car. The numbers 1, 2, 3, 4, and 5 represent the five categories 3.5, 3.2, 3.0, 2.2, and 1.8L, respectively.545512111351542131323412215531521225Prepare a frequency distribution table.Determine the percentages for all categories.What percentage of the senior citizens drive cars of category 1 or 3?
4 A manufacturing company of condenser retaining bolts for car engines implemented a quality control system. As part of this quality control system, a team of engineers decided to record the number of nonconforming bolts produced in each shift. The following data show the number of nonconforming bolts during the past 45 shifts.253026262516212221271524192024163028242315152128181521272628171924262717271922271625163018Prepare a complete frequency distribution table, that is, a table having frequency, relative frequency, percentage, and cumulative frequency columns.
5 The following data give the number of graduate students admitted in all engineering programs of a prestigious university during the past 30 years (1976–2005).148167171177175165134177168142126166130122157138163129143145141162147141164137149146132157Prepare a complete frequency distribution table, that is, a table having frequency, relative frequency, percentage, and cumulative frequency columns.
6 A
