Math Problem Statement

Richard has the following data:

x,16,16,20 If the mean is 17, which number could x be?

Solution

The mean (average) is given by:

Mean=Sum of all valuesTotal number of values\text{Mean} = \frac{\text{Sum of all values}}{\text{Total number of values}}

We have the numbers: x,16,16,20x, 16, 16, 20, and the mean is given as 17.

Step 1: Set Up the Equation

x+16+16+204=17\frac{x + 16 + 16 + 20}{4} = 17

Step 2: Solve for xx

x+524=17\frac{x + 52}{4} = 17

Multiply both sides by 4:

x+52=68x + 52 = 68

Subtract 52 from both sides:

x=16x = 16

Answer:

xx could be 16.

Would you like a further breakdown or more examples?

Related Questions:

  1. How do you calculate the median of a dataset?
  2. What happens to the mean if you add a new number to the dataset?
  3. How do you find the mode of a dataset?
  4. What is the range of the given dataset?
  5. Can the mean be higher than the highest number in the dataset?

Tip: The mean is sensitive to extreme values (outliers), which can significantly affect the average.

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Math Problem Analysis

Mathematical Concepts

Statistics
Mean (Average)

Formulas

Mean = (Sum of all values) / (Total number of values)

Theorems

Basic properties of the mean

Suitable Grade Level

Grades 6-8