Mean, median and mode

Example

 

Frequency and frequency tables

The frequency of a particulat data value is the number of times the data value occurs.

For example if 4 students have a score of 80 in mathematics and then the score of 80 is said to have a frequency of 4. The frequency of a data value is often represented by f.

A frequency table is constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies.

 

Example

The marks awarded for an assignment set for a Year 8 class of 20 students were as follows:
     6     7     5     7     7     8     7     6     9     7
     4     10   6     8     8     9     5     6     4     8

Present this information in a frequency table.

 

 

Solution

To construct a frequency table, we proceed as follows:

Step 1

Construct a table with three columns.  The first column shows what is being arranged in ascending order (i.e. the marks).  The lowest mark is 4.  So, start from 4 in the first column as shown below.

 

Mark     Tally          Frequency
4    
5    
6    
7    
8    
9    
10    

 

 

Step 2

Go through the list of marks.  The first mark in the list is 6, so put a tally mark against 6 in the second column. 

The second mark in the list is 7, so put a tally mark against 7 in the second column. 

The third mark in the list is 5, so put a tally mark against 5 in the third column as shown below.

Mark Tally Frequency
4    
5 /  
6 /  
7 /  
8    
9    
10    

We continue this process until all marks in the list are tallied.

 

Step 3

Count the number of tally marks for each mark and write it in third column. 

The finished frequency table is as follows:

Find the mean, median mode and range for the following list of values

13, 18, 13, 14, 13, 16, 21, 13

The mean is usually average, so:

(13 + 18 + 13 + 14 +13 + 14 + 13 + 16 + 21 + 13)/ 9 =15

Note that the mean isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers. 

 

The median is the middle value, so I'll have to rewrite the list in order.

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be

(9 + 1) + 2 = 10/2 =5th number.

13, 13, 13, 13, 14, 14, 16, 18, 21

So the median is 14.

 

The mode is the number that is repeated more often than any other number, so 13 is the mode. 

 

The largest value is 21, and the smallest is 13, so the range is 21 -13 = 8