Find the sum of the range and the mode of the set of numbers 10, 9, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 7, 10, 6, 5

To solve this problem, we need to determine the range and the mode of the given data set and then find their sum.

1. Analyze the Data

First, let's list the numbers in ascending order to make them easier to work with: 4, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10

2. Find the Range

The range is the difference between the highest value and the lowest value in a data set.

• Highest value = 10
• Lowest value = 4
• Range = $10 - 4 = 6$

3. Find the Mode

The mode is the number that appears most frequently in the data set. Let's count the frequency of each number:

• 4: appears 1 time
• 5: appears 1 time
• 6: appears 2 times
• 7: appears 3 times
• 8: appears 3 times
• 9: appears 4 times
• 10: appears 6 times

Since 10 appears the most (6 times), the mode is 10.

4. Calculate the Sum

The question asks for the sum of the range and the mode:

• Sum = Range + Mode
• Sum = $6 + 10 = 16$

Conclusion

Comparing our result to the options provided: A. 16 B. 14 C. 12 D. 10

The calculated sum is 16, which matches option A.

Exam Tip: When dealing with a long list of numbers, always arrange them in ascending order first. It prevents you from missing a number or miscounting the frequency, which is the most common cause of errors in statistics questions.