Question

Brittany has the following data:

95t14191161012
If the mode is 10, which number could t be?

Answer 1

To determine which number \( t \) could be to ensure that the mode of the data set \( 95, t, 14, 19, 11, 16, 10, 12 \) is 10, we need to analyze the condition for the mode.

The mode is the number that appears most frequently in a data set. For 10 to be the mode, it must appear more frequently than any other number in the list.

Currently, the provided numbers are:
- 10 appears 1 time
- 95 appears 1 time
- 14 appears 1 time
- 19 appears 1 time
- 11 appears 1 time
- 16 appears 1 time
- 12 appears 1 time

This means that all the numbers currently appear the same number of times (1 time each). Therefore, for 10 to become the mode, it must appear at least one more time than any other number.

If we let \( t \) equal 10, then 10 will appear twice, while every other number will still only appear once, making 10 the mode.

Thus, \( t \) could be:

\[
t = 10
\]

This situation allows \( 10 \) to be the mode. Any other value for \( t \) would result in 10 still being counted as appearing once, and no new number could match the single occurrence of \( 10 \) to change the mode.

In conclusion, the value of \( t \) that ensures the mode is 10 is:

\[
\boxed{10}
\]