Mean Frequency Table

In Statistics, mean is a basic term used frequently. A frequency table is one in which the mean and other terms can be determined. Basically, the frequency table consists of mean, median and mode. In this article, we shall discuss about the terms used in frequency table. Also we shall solve some sample problems based on mean of a frequency table.

Terms in a frequency Table:

Mean:
Mean is the method of the addition of values divided by the number of values in the given set of data.
Mean = addition of the given values / Entire number of values

Median:
Median is actually a middle number of a table. Some cases may have even values. In such cases, there will be 2 middle values. The median for such cases will be the average of the two vales.

Mode:
The most commonly repeated value in the given set of data is called as the mode for the given table..
Range:
The Variation between the greatest and the least values in the given set is said to be the range of the particular set.

Example problems for Mean Frequency Table:

Example 1:
Determine the mean, median, mode, and the range of the set of data given below.
13  17   15  16  22  25  22  27 14
Solution:
Given set of data can be arranged in the order.
13  14   15  16  17  22  22  25  27

Mean:
                Mean = ((13 + 14 + 15+ 16 + 17+ 22+ 22+ 25 + 27)/9)
                          = 171/9
                          = 19
              Median:
                  The middle number is 17. Hence the median is 17
              Mode:
                  Commonly repeated value is 22. Therefore mode is 22
              Range:
                  27 - 13 = 14.
The results are
                Mean = 19
              Median = 17
                Mode = 22
               Range = 14.

Example 2:
Consider the frequency distribution shown in scores of 20 students in a science test.
The mean of these marks = total marks /number of students
Frequency table:

Marks(x)	Frequency(f)
40	1
50	2
60	4
70	3
80	5
90	2
100	3
Total	20

                             
Then,  x = (40*1)+ (50*2)+ (60*4)+ (70*3)+ (80*5)+ (90*2)+ (100*3)
             =  40  + 100 + 240 + 210 + 400 + 180 + 300
             =  1470 / 20
             = 551 / 7
              = 73.5 marks

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    It will be very easy to discover the products of the scores and the frequencies by adding an extra column to the frequency table and the work as below:

Marks(x)	Frequency(f)	fx
40	1	40
50	2	50
60	4	240
70	3	210
80	5	400
90	2	180
100	3	300
Total	20	1470

                                                                
   Mean = sum of the xf column/ sum of the f column  
            = 1470/20

   Mean = 73.5 marks