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In statistics, the Frequency distribution is a continuous arrangement of the values that one or more variables take in a sample. When you write some entry in the table it contains the frequency within a particular interval. Measure of central tendency is used to summarise the data. It specifies the single most representative value to describe the given set of data. Arithmetic mean is the bery common method to calculate the average. It is based on the observations of th given data and is very easy to calculate. Median is the better summary of such data. Mode is used to find the qualitative data.
Measure of Central tendency
There are three most important methods to calculate the average. They are Mean, Median and Mode.
Arithematic Mean is defined as the sum of the values of all observation divided by the number of observation. Median is the middle value when the given set of data is arranged in ascending order. Mode is the most appropriate measure. It is value which occurs maximum number of times. Now, we will look upon the calculation of continuous frequency distribution.
How to calculate the Continuous Frequency Distribution.
We are having four steps to calculate the continuous frequency distribution-
Should have equal or unequal-sized class intervals.
There are two conditions of unequal class interval sizes. They are: When we have data on income and other related variables where the range is very high. If many values are present in a small part of the range, using class intervals with equal sizes would lead to a loss of information on various values. Except for the case we discussed, we can define class intervals of equal sizes in frequency distributions.
How many classes should we have.
It depends on the total number of observations. So, the number of classes could be between 6 and 15. Therefore, if we are using equal-sized class intervals, we can calculate the number of classes by dividing the range by the size of the class intervals.
What should be the size of each class.
When we know the class interval which is based on the range of the variable, then we can find the number of classes. Thus, we can see that these two are interlinked. Therefore, we have to decide about them simultaneously.
How should we determine the class limits
Class limits should be definite and explicitly stated. For example, we have two types of class intervals, such as Exclusive class intervals: In this type of class interval, an observation equal to either the upper or the lower class limit is excluded from the frequency of the class. Inclusive class intervals: Here, values that are equal to the lower and upper limits of a class are included in the frequency of the same class.
Continuous frequency distribution table examples-
Question- Consider the given table. Calculate the value of mode.
data | Cumulative Frequency |
Less than 50 | 97 |
less than 45 | 95 |
Less than 40 | 90 |
Less than 35 | 80 |
Less than 30 | 60 |
Less than 25 | 30 |
Less than 20 | 12 |
Less than 15 | 4 |
Ans- We know that it is the case of cumulative frequency distribution.
To calculate the mode, first convert into exclusive series. Here, the series is in descending order. The
table has to be converted into normal frequency table.
data group | Frequency |
45-50 | 97-95=2 |
40-45 | 95-90=5 |
35-40 | 90-80=10 |
30-35 | 80-60=20 |
25-30 | 60-30= 30 |
20-25 | 30-12=18 |
15-20 | 12-4=8 |
10-15 | 4 |
The value of mode lies in 25-30 class interval.
Here, Lower limit of modal class(L) = 25
Difference between the frequency of the modal class and frequency of the the class preceding the modal class (D1)= 30-18=12
Difference between the frequency of the modal class and the frequency of the class succeeding the modal class (D2)= 30-20=10
Class interval (h)= 5
The value of mode = L + D1D1+D2h= 25+ 1212+105
= 27.27
Hence, the mode is 27.27
What is a class frequency?
A class frequency is defined as the number of times the data in the given class interval is repeated in the
series. To make a frequency distribution table, you have to create the table by using the tally marks. This is the easiest way to calculate the frequency distribution table.
Conclusion-
Discrete and Continuous Variables were defined in the article. We have even discussed the frequency distributions. We have explained the frequency distribution table in-depth with the solved example to understand the concept better. We have talked about the class frequency, mean deviation as well as standard deviation. We already know that the measure of central tendency summaries the data with the single value which represents the entire data. The sum of deviations of items from the arithmetic mean is equal to zero. it is important to assign weights to various items according to their importance.
