How to make a frequency table, Class Interval

Presentation of data in frequency distribution is one of the first steps that is usually done in analyzing a data. Interpretation of data can usually be made easier if the data is organized and simplified first into a table. One of them is with frequency table. Frequency distribution is a table, where data is grouped into several numerical intervals called class intervals. The form of this table is very simple because it only presents the number of observations or frequencies in each class interval.
Frequency table is a table that shows the distribution or distribution of data frequencies that we have, which are composed of frequencies for each class or category that have been set. The frequency of each class / category shows the number of observations in the class category concerned.
To clarify the above description, we consider the frequency table as shown by the following table,

How to make a frequency table, Class Interval

By studying the frequency table above, at least the description of the amount of capital owned by 50 companies in New York can be known precisely, at least we know immediately the distribution of company categories based on the amount of capital owned by this frequency distribution, especially the distribution of theoretical frequencies, plays a role important in statistical analyzes and conclusions.
The process of compiling data into a frequency distribution is very simple but quite tedious and time-consuming if done manually. The stages needed in the preparation of frequency distribution with class which is an interval / interval is done in 4 steps namely;

Determination of the number of class intervals

The number of class intervals, whether later making these tables using computer assistance or not, we ourselves must determine. The number of class intervals depends on the intent and purpose we make the frequency table and the number of observations of the variables we have.
Observations that are not too many certainly do not require a lot of class intervals, on the contrary large observations require quite a lot of classes. However, so that the number of class intervals obtained is easier to adjust, use the following formula:
k = 1 + 3.3 log (n2/100)
The formula is a modification of the Sturger formula, k = 1 + 3.3 log (n).

The number of class intervals is also very dependent on the number of observations in the data. The greater the amount of data, the more number of classes required. However, it is usually recommended that the number of class intervals range from 5 to 15 classes for a number of n between 50 and 1000. If the number of class intervals used is too small, then we do not have much additional information obtained from the grouping. Likewise, if the number of class intervals is too much, then grouping data into class intervals will not provide maximum benefit.

Determination of Class Intervals

The interval in class or width depends on the number of classes chosen and the range of data. One thing to note, not to complicate in interpreting the frequency table, it is recommended that all class intervals have the same class interval or class width.
Determination of the width of the class interval is done by first determining the range (Range) of the data, which is the difference between the highest observation data with the lowest observation data, then dividing it by the number of intervals desired.
R = Xb - Xk
Note:       R = range 
              Xb = largest data
              Xk = smallest data
Next, the intervals in the class we represent with I are determined by the formula:
I = R / k

Determination of Class Interval Limits.

The boundaries between class intervals must be clearly defined and not overlap so that the values ​​of observations can be grouped into each class, except for open class intervals. Each class must have a lower limit and upper limit of the class. The lower limit of the first class interval is usually the minimum value of the data. While the upper limit of the last class interval is determined such that the maximum value of the data lies in the last class interval.
A class is called an open class interval if the class has no lower or upper limits. Open class intervals are usually used if the data analyzed has very large diversity and most observations are concentrated in a relatively small range.

Determination of frequency for each class interval.

Determination of the frequency for each class we will discuss here is if we do it manually without the help of a computer.
There are two events that can be used in determining the frequency of each class:
First, we rearrange the data in sequence from the smallest to the largest or vice versa. Next we count the number of observations including the first, second, and so on class intervals up to the last class interval.
Second, Enter the data one by one starting from the first observation into the class in accordance with marking the class.
Example of Making a Frequency Table
The data of Mathematics Insurance student subject X is known in the range of 0-100, with the highest value obtained is 98 and the lowest is 34. Where the data is as follows:

79, 49, 88, 74, 81, 98, 87, 80, 80, 35, 48, 70, 91, 93, 87, 75, 68, 60, 76, 38, 56, 43, 74, 86, 90, 91, 83, 51, 65, 59, 71, 63, 63, 93, 88, 80, 68, 79, 75, 55, 69, 59, 73, 63, 79, 44, 89, 34, 85, 95.

From the data set above to create a Frequency Table, the steps that must be taken are:
Determination of the number of class intervals
To determine the number of classes of values ​​that must be known in advance is the number of collected values ​​is 50. If n = 50 is substituted into the formula to be,
Number of classes = 1 + (3.3) log 50 = 1 + 6.6 ≈ 7

Determination of Class Intervals
As is known the greatest value obtained from the Mathematics Insurance courses is 98 and the smallest is 34. So, 
R = Xb - Xk = 98 – 34 = 64
I = R / k = 64 / 6.6 = 9.7 ≈ 10.
The number 10 is the width of the class that must be made, for example, from grades 34 to (34 + 10) (counting starts from 34, 35, 36, 37 ..., 34).
From the calculation results above, the table can be presented as below,
Class
Number of Students (fi)
Frequency(%)
34 – 43
4
8 = (4/50) x 100
44 – 53
4
8
54 – 63
8
16
64 – 73
7
14
74 – 83
13
26
84 – 93
12
24
94 – 103
2
4
Total
50
100

Note: To get the number of students and the frequency it is better to arrange the data in advance can be manually or using Excel software.

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