Q. 33.8( 19 Votes )

Let us find the mode of data given below :

i. 8, 5, 4, 6, 7, 4, 4, 3, 5, 4, 5, 4, 4, 5, 5, 4, 3, 3, 5, 4, 6, 5, 4, 5, 4, 5, 4, 2, 3, 4

ii. 15, 11, 10, 8, 15, 18, 17, 15, 10, 19, 10, 11, 10, 8, 19, 15, 10, 18, 15, 3, 16, 14, 17, 2

Answer :

Since, mode is the set of data values that appears most often in the data.

(i). Arranging the data values in ascending order to make observation easier, we get


2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 8


Note the appearances now,


1 appears 1 time


3 appears 4 times


4 appears 12 times


5 appears 9 times


6 appears 2 times


7 appears 1 time


8 appears 1 time


4 appears most of the times, that is, 12 times.


Thus, mode is 4.


(ii). Arranging the data values in ascending order to make observation easier, we get


2, 3, 8, 8, 10, 10, 10, 10, 10, 10, 11, 11, 14, 15, 15, 15, 15, 15, 17, 17, 18, 18, 19, 19


Note the appearances now,


2 appears 1 time


3 appears 1 time


8 appears 2 times


10 appears 6 times


11 appears 2 times


14 appears 1 time


15 appears 5 times


17 appears 2 times


18 appears 2 times


19 appears 2 times


10 appears most of the time, that is, 6 times.


Thus, mode is 10.


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