High School

Look at this set of 9 numbers:

[tex]\[
\begin{array}{lllllllll}
76 & 67 & 39 & 15 & 67 & 76 & 84 & 67 & 60 \\
\end{array}
\][/tex]

How would the mode change if the number 76 replaced one of the 67s in the set?

A. Increase
B. Decrease
C. No change

Answer :

Sure! Let's go through the solution step by step for the given set of numbers:

Original set of numbers:
76, 67, 39, 15, 67, 76, 84, 67, 60

1. Find the mode of the original set:

- The mode is the number that appears most frequently in a set of numbers.
- In this set, the number 67 appears three times, which is more than any other number. Therefore, the mode is 67.

2. Modify the set by replacing one of the 67's with 76:

- Original set: 76, 67, 39, 15, 67, 76, 84, 67, 60
- Modified set: 76, 76, 39, 15, 67, 76, 84, 67, 60
- Here, we replaced one instance of 67 with 76.

3. Find the mode of the modified set:

- In the modified set, the number 76 now appears three times, while 67 appears only twice.
- Therefore, the mode of the modified set is 76.

4. Determine how the mode has changed:

- Originally, the mode was 67.
- After the change, the mode is 76.
- Since the original mode changed from 67 to a new value of 76, we consider this an "increase" in the value of the mode.

Thus, when one of the 67's is replaced with 76, the mode changes from 67 to 76, indicating an "increase."

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