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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