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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