Math Problem Statement
Solution
The problem asks us to find the new mean of a set of numbers after adding two additional numbers. Here's the step-by-step solution:
Problem Details:
- A set of 5 numbers has a mean of 7.31.
- The numbers 4.47 and 10.15 are added to this set.
- Find the mean of the new set.
Step 1: Total sum of the original set
The formula for the mean is:
Rearranging to find the sum of the original set:
Substitute the given values:
Step 2: Total sum after adding the two new numbers
Add the two new numbers to the original sum:
Step 3: Total number of numbers in the new set
The original set had 5 numbers, and 2 more were added:
Step 4: Calculate the new mean
The new mean is:
Substitute the values:
Final Answer:
The mean of the new set of numbers is 7.31.
Would you like further explanation or to explore related concepts?
Related Questions:
- What is the significance of the mean in a data set?
- How does adding extreme values (outliers) affect the mean?
- Can you derive the median from the given data?
- How would the solution change if only one additional number was added?
- What happens to the mean if all values in a data set are increased by the same constant?
Tip: Always verify that you're dividing by the correct total number of elements in such problems!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Arithmetic Mean
Averages
Basic Arithmetic
Formulas
Mean = Sum of numbers / Number of numbers
Sum of original set = Mean × Number of numbers
Theorems
-
Suitable Grade Level
Grades 6-8