Question

Observe the data and answer the questions that follow:

16, 15, 16, 16, 8, 15, 17

1. Which data value can be put in the data so that the mode remains the same?
2. At least how many and which value(s) must be put in to change the mode to 15?
3. What is the least number of data values that must be put in to change the mode to 17? Name them.

Answer 1

Given data; 16, 15, 16, 16, 8, 15, 17

Arranging the given data in ascending order, we have 8, 15, 15, 16, 16, 16, 17

a. As per the given data, 16 is the mode of data, since it has highest frequency, i.e. 3

Now, if 15 is added to the given data, mode will get changed to 15 and 16, whereas if any other number, i.e. 8, 16 or 17 is added, mode will remain same.

b. Atleast two 15’s should be added to change the mode to 15. On adding two 15’s the frequency of 15 will be maximum, i.e. 4.

c. We will have to add atleast three 17’s to change the mode to 17. On adding three 17’s, the frequency of 17 will be maximum, i.e. 4.