Math Problem Statement

Suppose the mean of a data set was 83. If 15 were added to each number in the data set, what would be the new mean?

Solution

The question asks for the new mean if 15 were added to each number in the data set.

Given:

  • The original mean is 83.
  • If 15 is added to each value, the new mean will simply be the original mean plus 15.

Thus, the new mean is: New Mean=83+15=98\text{New Mean} = 83 + 15 = 98

It looks like the provided answer is 97, but the correct answer is 98. Would you like to know more details or have any other questions?

Here are five related questions:

  1. How does adding a constant to every number in a data set affect the mean?
  2. What happens to the mean if you multiply every value in a data set by a constant?
  3. How would the standard deviation change if a constant were added to each number in the data set?
  4. What would be the new mean if you added 20 instead of 15 to each value?
  5. How would removing an outlier affect the mean of a data set?

Tip: Adding or subtracting the same constant to every value in a data set shifts the mean by that same amount.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Mean
Addition of Constants to Data Sets

Formulas

New Mean = Original Mean + Constant Added

Theorems

If a constant is added to every element of a data set, the mean increases by that constant.

Suitable Grade Level

Grades 6-8