Question

Find the value of K for which the mode of the following data is 7. 

3, 5, 5, 7, 3, 6, 7, 9, 6, 7, 3, 5, 7, 3, К

Answer 1

Given: The data set is 3, 5, 5, 7, 3, 6, 7, 9, 6, 7, 3, 5, 7, 3, K.

Step-wise calculation:

1. Count occurrences (excluding K):

3 appears 4 times.

5 appears 3 times.

6 appears 2 times.

7 appears 4 times.

9 appears 1 time.

2. For 7 to be the (unique) mode its frequency must exceed all others.

3. If K = 7, frequency (7) = 5 while frequency (3) remains 4 → 7 becomes the unique mode.

4. Any other choice of K:

K = 3 would have 5 occurrences (mode becomes 3).

K = 5, 6, 9 or a new value → 7 and 3 remain tied at 4 (no unique mode 7).

K = 7.