Math Problem Statement

A un conjunto de 5 números cuya media es 7.31 se le añaden los números 4.47 y 10.15. ¿Cuál es la media del nuevo conjunto de números?

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:

Mean=Sum of numbersNumber of numbers\text{Mean} = \frac{\text{Sum of numbers}}{\text{Number of numbers}}

Rearranging to find the sum of the original set:

Sum of the original set=Mean×Number of numbers\text{Sum of the original set} = \text{Mean} \times \text{Number of numbers}

Substitute the given values:

Sum of the original set=7.31×5=36.55\text{Sum of the original set} = 7.31 \times 5 = 36.55


Step 2: Total sum after adding the two new numbers

Add the two new numbers to the original sum:

New total sum=36.55+4.47+10.15=51.17\text{New total sum} = 36.55 + 4.47 + 10.15 = 51.17


Step 3: Total number of numbers in the new set

The original set had 5 numbers, and 2 more were added:

New total count of numbers=5+2=7\text{New total count of numbers} = 5 + 2 = 7


Step 4: Calculate the new mean

The new mean is:

New mean=New total sumNew total count of numbers\text{New mean} = \frac{\text{New total sum}}{\text{New total count of numbers}}

Substitute the values:

New mean=51.177=7.31\text{New mean} = \frac{51.17}{7} = 7.31


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:

  1. What is the significance of the mean in a data set?
  2. How does adding extreme values (outliers) affect the mean?
  3. Can you derive the median from the given data?
  4. How would the solution change if only one additional number was added?
  5. 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