Question

The mode of the data is 7, find the value of k.(2 ,4 ,6, 7, 5, 6 ,10 ,6, 7 , 2k+1, 9, 7, 13)

Answer 1

The Mode of a set of observations is the observation that occurs most often.

The given observations are

2, 4, 6, 7, 5, 6, 10, 6, 7, 2k+1, 9, 7, 13

Thus we obtain the following table

Observations	Occurrence
2	1
4	1
5	1
6	3
7	3
9	1
10	1
13	1

Also given that mode of the data is 7.

We see that the observation 6 and 7 has occurred 3 times. Since the mode is 7, the occurrence of observation 7 should be more than observation 6. Hence, in 2K + 1 the value of k will be 3, which gives;

= 2K + 1

When k = 3,

= 2(3) + 1

= 6 + 1

= 7.

Therefore, the value of k is 3.