Math Problem Statement

Which of the distributions is likely to have the largest mean?

Solution

In the given image, eight different distributions are presented (A to H), and the question asks which distribution is likely to have the largest mean.

Observing each distribution:

  • A: Skewed slightly to the right, but generally centered around 1.5.
  • B: Symmetric, centered near 0.
  • C: Symmetric distribution with a mean close to 0.
  • D: Symmetric, centered around 15.
  • E: Symmetric, centered around -2.
  • F: Right-skewed, most values concentrated between 0 and 8.
  • G: Symmetric, centered around 5.
  • H: Skewed to the left, with most values centered near -2.

Answer:

The distribution likely to have the largest mean is D, as it is centered around 15, which is higher than the means of other distributions that are centered near smaller values (such as A, B, or C) or even negative values (like E or H).

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Math Problem Analysis

Mathematical Concepts

Statistics
Mean
Distribution
Skewness

Formulas

Mean = Sum of all values / Number of values

Theorems

Basic properties of distribution (skewness and symmetry)

Suitable Grade Level

Grades 9-12