Skip to main content

CONSTRUCTING THE FREQUENCY DISTRIBUTION TABLE



The frequency distribution table is a table that divides data into groups (classes) and shows how many data values occur in each group/class. Below is an example of frequency distribution table.


Now we are learning how to create a frequency distribution table.

Suppose we have a collection of ungrouped data on last year’s advertising expenditures of 40 logistics companies, recorded in millions Rupiahs.



To construct a frequency distribution table of the ungrouped data, apply the following steps.

Step 1: Find the range of the data
The range (R) is defined as the difference between the largest data and the smallest data. In this case, R = 307 - 242 = 65.

Step 2: Determine the number of categories/classes (k)
Applying Sturges rule (k = 1 + 3,322 log n, where n = the number of data), we have:
$k = 1 + 3.322 \: log \: 40 \approx 6.32$
As the value of k must be a natural number, 6.32 is rounded up to 7, so k = 7.

Step 3: Determine the class width (c)
To find c, use $c = \frac{R}{k}$. The number of decimal places of c must be the same as the original data. If all the original data are whole numbers then c must be a whole number. If the data are accurate to 1 decimal place, then c must have 1 decimal place. If the data have 2 decimal places, then c must have 2 decimal places, etc. In case the c as previously calculated does not have the same number of decimal places as the original data, we have to round  the c value up. Make sure that the result of the rounding up has the same number of decimal places as the original data. In this example, $c = \frac{65}{7} \approx 9.2857$. As the original data are whole numbers, the c value must be a whole number. But the rounding must be up, so c = 10.

Step 4: Determine the class intervals of each class
As the smallest data in this example is 242 and the class width (as determined above) is 10, we may determine that the first class interval is 242 - 251. Then, the second class must be 252 - 261. Continuing this way, we will have the following list of class intervals.



Alternatively, we may construct other class intervals such as:


or



No matter which one we choose as set of class intervals, make sure that each of the original data can be classified into one and only one (interval) class in the grouping.

Step 5: Determine the number of observations falling into each class interval
In other words, we find the class frequencies in this step. Assuming we choose the last alternative among the three alternatives of grouping mentioned above, we get the following frequency distribution table.


Exercise 1
Referring to the example above, create the frequency distribution tables based on the other two alternatives of grouping.
Exercise 2
A researcher has collected some data on the distance (in kilometers) from people's residence in a certain district to the nearest newsstand. The data are presented as follows.


Based on the data, create a frequency distribution table with equal class widths. Apply the Sturges rule in determining the number of classes.





Comments

Post a Comment

Popular posts from this blog

THE QUARTILES AND MEDIAN OF GROUPED DATA

In this post,  we will learn how to determine the quartiles when some quantitative data are presented in a frequency distribution table. For example, we have the following data, showing Flesch Readability Score of 80 monthly bulletin articles published by Britt and Co. Ltd. Find the quartiles of these readability scores. To answer this, first augment the table with a new column to the right of the frequency column, namely Data Numbers column. There are 5 data in the first class, so the class contains data no. 1 to  no. 5. There are 7 data in the second class, so the class contains data no. 6 to no. 12. There are 13 data in the third class, so the class contains data no. 13 to no. 25. Continuing this way, we get the following: In this case, finding the first quartile means finding the  20 th  data, after the data have been ordered from the smallest to the highest (20 = ¼ x 80). Note that the  20 th  data is in the third class (20 is in the range of 13 - 25, as s
Post a Comment
Read more

CALCULATING THE MEAN OF GROUPED DATA

Sometimes quantitative data are presented in the form of a frequency distribution table (FDT). A typical FDT is as follows. Suppose that the table above presents the duration of 16 cell phone conversations between pairs of teens. There are 2 conversations with duration from 30 seconds to 44 seconds, 3 conversations with duration from 45 seconds to 59 seconds, etc. How do we calculate the mean of the data? Step 1: Determine the midpoint of each class If M i denotes the midpoint of class i, $M_{i} = \frac{LB_{i}+UB_{i}}{2}$ where  LB i  = lower bound of class i and  UB i  = upper bound of class i. The lower bounds of class 1, 2, 3, 4, 5 are 30, 45, 60, 75, 90, respectively and the upper bounds are 44, 59, 74, 89, 104, respectively. Then, $M_{1} = \frac{30+44}{2} = 37$.  Similarly, $M_{2} = \frac{45+59}{2} = 52$. Continuing this way, we have the following table. Step 2: Multiply each class frequency f i by the corresponding class midpoint M i , resulting in f i M
Post a Comment
Read more