Given the following data , calculate mode using the grouping technique .
`{:("Size",2,3,4,5,6,7,8,9,10,11,12,13),("Frequency",3,8,10,12,16,14,10,8,17,5,4,1):}`

Explanation

Check the following Tables 1 and 2 and the subsequent details. There are 6 columns in the table on the frequency and its groupings , as in Table 1.
In Column I, the frequencies as given in the question are noted agianst the respective items.
In Column II, the frequencies are grouped in twos beginning with the item.
In Column III, the frequencies are grouped in twos beginning with 2nd item .
In Column Iv , the frequencies are frouped into threes beginning with 1st item.
In Column V the frequencies are frouped into threes beginning with 2nd item.
In Column VI , the frequencies are grouped into threes beginning with 3rd item.
Highest value in all the columns are shown in bold letters or are underlined, or encircled .

Analysis Table shows those items corresponding to which there are highest frequencies in different columns . Thus , in column I Column the highest total is 17 and this corresponds to the item 10. For column I a tick mark (`root`) is accordingly noted against 10 in the Analysis Table . Likewise , in column II the highest total is 30 and this corresponds to the items 6 and 7 (bracketed). A tick mark (True) is accordingly noted aginst 6 as well as 7 in the Analysis Table.
Similarly , in column III the highest total is 28 and it corresponds to the items 5 and 6. Thus , a tick mark is noted aginst 5,6 , and 7 in column IV . Likewise , tick mark are noted in other columns . the Anakysis Tabl shows that item 6 item 6 has the largest number of tick marks . thus , the Mode (Z) =6.