FREQUENCY TABLE

In this Chapter we will discuss how to create a frequency table and calculate cumulative frequency and relative frequency.

Let us consider the following example:

# Enter the data
data=c(24,23,17,13,25,30,22,28,38,39,1,4,9,2,10,7,36,
       14,3,31,33,37,11,19,15,16,29,35,27,26)

# Find out the minimum and maximum of the data
summary(data)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1.00   11.50   22.50   20.80   29.75   39.00 

# create class intervals
breaks=seq(0,40,5)

# create frequencies
freq=cut(data,breaks)

# conver the frequencies as a table
freq=table(freq)
freq

freq
  (0,5]  (5,10] (10,15] (15,20] (20,25] (25,30] (30,35] 
      4       3       4       3       4       5       3 
(35,40] 
      4 

# Calculate total frequencies
N=sum(freq)

# calculate cumulative frequencies
cum.freq=cumsum(freq)

# calculate relative frequencies
rel.freq=freq/N

# combine all calculated values in one table
cbind(freq,cum.freq,rel.freq)

        freq cum.freq  rel.freq
(0,5]      4        4 0.1333333
(5,10]     3        7 0.1000000
(10,15]    4       11 0.1333333
(15,20]    3       14 0.1000000
(20,25]    4       18 0.1333333
(25,30]    5       23 0.1666667
(30,35]    3       26 0.1000000
(35,40]    4       30 0.1333333

barplot(freq, xlab = "Class Intervals", ylab = "Frequencies")

Exercise:

1. Construct a frequency table from the following data- 46 40 29 24 8 3 33 49 17 35 28 34 27 43 26 37 4 5 42 10 22 13 19 9 41 14 11 50 36 32 30 47 12 44 38 15 31 7 23 25

2. Construct a frequency table from the following data and draw the bar diagram. 40 21 2 44 17 13 49 46 28 6 20 19 37 50 41 1 4 7 38 32 3 25 39 34 14 22 27 26 30 5 31 45 23 11 8 29 24 18 47 42 9 33 48 36 15

Try Yourself